Symmetry

7 pages, 211 KiB

Open AccessArticle

Single-Route Linear Catalytic Mechanism: A New, Kinetico-Thermodynamic Form of the Complex Reaction Rate

by Gregory S. Yablonsky, Denis Constales and Guy B. Marin

Symmetry 2020, 12(10), 1748; https://doi.org/10.3390/sym12101748 - 21 Oct 2020

Cited by 5 | Viewed by 1706

For a complex catalytic reaction with a single-route linear mechanism, a new, kinetico-thermodynamic form of the steady-state reaction rate is obtained, and we show how its symmetries in terms of the kinetic and thermodynamic parameters allow better discerning their influence on the result. [...] Read more.

For a complex catalytic reaction with a single-route linear mechanism, a new, kinetico-thermodynamic form of the steady-state reaction rate is obtained, and we show how its symmetries in terms of the kinetic and thermodynamic parameters allow better discerning their influence on the result. Its reciprocal is equal to the sum of n terms (n is the number of complex reaction steps), each of which is the product of a kinetic factor multiplied by a thermodynamic factor. The kinetic factor is the reciprocal apparent kinetic coefficient of the i-th step. The thermodynamic factor is a function of the apparent equilibrium constants of the i-th equilibrium subsystem, which includes the

(n - 1)

other steps. This kinetico-thermodynamic form separates the kinetic and thermodynamic factors. The result is extended to the case of a buffer substance. It is promising for distinguishing the influence of kinetic and thermodynamic factors in the complex reaction rate. The developed theory is illustrated by examples taken from heterogeneous catalysis. Full article

(This article belongs to the Special Issue Symmetry and Complexity of Catalysis in Flow Chemistry)

18 pages, 3737 KiB

Open AccessArticle

A Novel Centrality for Finding Key Persons in a Social Network by the Bi-Directional Influence Map

by Chin-Yi Chen and Jih-Jeng Huang

Symmetry 2020, 12(10), 1747; https://doi.org/10.3390/sym12101747 - 21 Oct 2020

Viewed by 1714

Abstract

Symmetry is one of the important properties of Social networks to indicate the co-existence relationship between two persons, e.g., friendship or kinship. Centrality is an index to measure the importance of vertices/persons within a social network. Many kinds of centrality indices have been [...] Read more.

Symmetry is one of the important properties of Social networks to indicate the co-existence relationship between two persons, e.g., friendship or kinship. Centrality is an index to measure the importance of vertices/persons within a social network. Many kinds of centrality indices have been proposed to find prominent vertices, such as the eigenvector centrality and PageRank algorithm. PageRank-based algorithms are the most popular approaches to handle this task, since they are more suitable for directed networks, which are common situations in social media. However, the realistic problem in social networks is that the process to find true important persons is very complicated, since we should consider both how the influence of a vertex affects others and how many others follow a given vertex. However, past PageRank-based algorithms can only reflect the importance on the one side and ignore the influence on the other side. In addition, past algorithms only view the transition from one status to the next status as a linear process without considering more complicated situations. In this paper, we develop a novel centrality to find key persons within a social network by a proposed synthesized index which accounts for both the inflow and outflow matrices of a vertex. Besides, we propose different transition functions to represent the relationship from status to status. The empirical studies compare the proposed algorithms with the conventional algorithms and show the differences and flexibility of the proposed algorithm. Full article

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17 pages, 2140 KiB

Open AccessArticle

Joint Entity-Relation Extraction via Improved Graph Attention Networks

by Qinghan Lai, Zihan Zhou and Song Liu

Symmetry 2020, 12(10), 1746; https://doi.org/10.3390/sym12101746 - 21 Oct 2020

Cited by 13 | Viewed by 3020

Abstract

Joint named entity recognition and relation extraction is an essential natural language processing task that aims to identify entities and extract the corresponding relations in an end-to-end manner. At present, compared with the named entity recognition task, the relation extraction task performs poorly [...] Read more.

Joint named entity recognition and relation extraction is an essential natural language processing task that aims to identify entities and extract the corresponding relations in an end-to-end manner. At present, compared with the named entity recognition task, the relation extraction task performs poorly on complex text. To solve this problem, we proposed a novel joint model named extracting Entity-Relations viaImproved Graph Attention networks (ERIGAT), which enhances the ability of the relation extraction task. In our proposed model, we introduced the graph attention network to extract entities and relations after graph embedding based on constructing symmetry relations. To mitigate the over-smoothing problem of graph convolutional networks, inspired by matrix factorization, we improved the graph attention network by designing a new multi-head attention mechanism and sharing attention parameters. To enhance the model robustness, we adopted the adversarial training to generate adversarial samples for training by adding tiny perturbations. Comparing with typical baseline models, we comprehensively evaluated our model by conducting experiments on an open domain dataset (CoNLL04) and a medical domain dataset (ADE). The experimental results demonstrate the effectiveness of ERIGAT in extracting entity and relation information. Full article

(This article belongs to the Section Computer)

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16 pages, 2495 KiB

Open AccessArticle

Improving the Results of the Earned Value Management Technique Using Artificial Neural Networks in Construction Projects

by Amirhossein Balali, Alireza Valipour, Jurgita Antucheviciene and Jonas Šaparauskas

Symmetry 2020, 12(10), 1745; https://doi.org/10.3390/sym12101745 - 21 Oct 2020

Cited by 12 | Viewed by 4347

Abstract

The cost, time and scope of a construction project are key parameters for its success. Thus, predicting these indices is indispensable. Correct and accurate prediction of cost throughout the progress of a project gives project managers the chance to identify projects that need [...] Read more.

The cost, time and scope of a construction project are key parameters for its success. Thus, predicting these indices is indispensable. Correct and accurate prediction of cost throughout the progress of a project gives project managers the chance to identify projects that need revision in their schedules in order to result in the maximum benefit. The aim of this study is to minimize the shortcomings of the Earned Value Management (EVM) method using an Artificial Neural Network (ANN) and multiple regression analysis in order to predict project cost indices more precisely. A total of 50 road construction projects in Fars Province, Iran, were selected for analysis in this research. An ANN model was used to predict the projects’ cost performance indices, thereby creating a more accurate symmetry between the predicted and actual cost by considering factors that influence project success. The input data of the ANN model were analysed in MATLAB software. A multiple regression model was also used as another analytical tool to validate the outcome of the ANN. The results showed that the ANN model resulted in a lower Mean Squared Error (MSE) and a greater correlation coefficient than both the traditional EVM model and the multiple regression model. Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models)

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21 pages, 5198 KiB

Open AccessArticle

Diffusion-Limited Reaction Kinetics of a Reactant with Square Reactive Patches on a Plane

by Changsun Eun

Symmetry 2020, 12(10), 1744; https://doi.org/10.3390/sym12101744 - 21 Oct 2020

Cited by 1 | Viewed by 2274

Abstract

We present a simple reaction model to study the influence of the size, number, and spatial arrangement of reactive patches on a reactant placed on a plane. Specifically, we consider a reactant whose surface has an N × N square grid structure, with [...] Read more.

We present a simple reaction model to study the influence of the size, number, and spatial arrangement of reactive patches on a reactant placed on a plane. Specifically, we consider a reactant whose surface has an N × N square grid structure, with each square cell (or patch) being chemically reactive or inert for partner reactant molecules approaching the cell via diffusion. We calculate the rate constant for various cases with different reactive N × N square patterns using the finite element method. For N = 2, 3, we determine the reaction kinetics of all possible reactive patterns in the absence and presence of periodic boundary conditions, and from the analysis, we find that the dependences of the kinetics on the size, number, and spatial arrangement are similar to those observed in reactive patches on a sphere. Furthermore, using square reactant models, we present a method to significantly increase the rate constant by sequentially breaking the patches into smaller patches and arranging them symmetrically. Interestingly, we find that a reactant with a symmetric patch distribution has a power–law relation between the rate constant and the number of reactive patches and show that this works well when the total reactive area is much less than the total surface area of the reactant. Since our N × N discrete models enable us to examine all possible reactive cases completely, they provide a solid understanding of the surface reaction kinetics, which would be helpful for understanding the fundamental aspects of the competitions between reactive patches arising in real applications. Full article

(This article belongs to the Special Issue Advances in Theoretical and Computational Chemistry)

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11 pages, 2556 KiB

Open AccessArticle

Circular Intensely Orthogonal Double Cover Design of Balanced Complete Multipartite Graphs

by M. Higazy, A. El-Mesady, Emad E. Mahmoud and Monagi H. Alkinani

Symmetry 2020, 12(10), 1743; https://doi.org/10.3390/sym12101743 - 21 Oct 2020

Cited by 5 | Viewed by 1901

Abstract

In this paper, we generalize the orthogonal double covers (ODC) of

K_{n, n}

as follows. The circular intensely orthogonal double cover design (CIODCD) of

X = K_{\underset{m}{\underset{︸}{n, n, \dots, n}}}

is defined as a collection [...] Read more.

In this paper, we generalize the orthogonal double covers (ODC) of

K_{n, n}

as follows. The circular intensely orthogonal double cover design (CIODCD) of

X = K_{\underset{m}{\underset{︸}{n, n, \dots, n}}}

is defined as a collection

T = {G_{0_{0}}, G_{1_{0}}, \dots, G_{{(n - 1)}_{0}}} \cup {G_{0_{1}}, G_{1_{1}}, \dots, G_{{(n - 1)}_{1}}}

of isomorphic spanning subgraphs of

X

such that every edge of

X

appears twice in the collection

T,

|E (G_{i_{0}}) \cap E (G_{j_{0}})| = |E (G_{i_{1}}) \cap E (G_{j_{1}})| = 0, i \neq j and |E (G_{i_{0}}) \cap E (G_{j_{1}})| = λ = (\begin{array}{l} m \\ 2 \end{array}), i, j \in ℤ_{n} .

We define the half starters and the symmetric starters matrices as constructing methods for the CIODCD of

X

. Then, we introduce some results as a direct application to the construction of CIODCD of

X

by the symmetric starters matrices. Full article

(This article belongs to the Section Mathematics)

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15 pages, 3284 KiB

Open AccessArticle

An Effective and Improved CNN-ELM Classifier for Handwritten Digits Recognition and Classification

by Saqib Ali, Jianqiang Li, Yan Pei, Muhammad Saqlain Aslam, Zeeshan Shaukat and Muhammad Azeem

Symmetry 2020, 12(10), 1742; https://doi.org/10.3390/sym12101742 - 21 Oct 2020

Cited by 23 | Viewed by 4209

Abstract

Optical character recognition is gaining immense importance in the domain of deep learning. With each passing day, handwritten digits (0–9) data are increasing rapidly, and plenty of research has been conducted thus far. However, there is still a need to develop a robust [...] Read more.

Optical character recognition is gaining immense importance in the domain of deep learning. With each passing day, handwritten digits (0–9) data are increasing rapidly, and plenty of research has been conducted thus far. However, there is still a need to develop a robust model that can fetch useful information and investigate self-build handwritten digit data efficiently and effectively. The convolutional neural network (CNN) models incorporating a sigmoid activation function with a large number of derivatives have low efficiency in terms of feature extraction. Here, we designed a novel CNN model integrated with the extreme learning machine (ELM) algorithm. In this model, the sigmoid activation function is upgraded as the rectified linear unit (ReLU) activation function, and the CNN unit along with the ReLU activation function are used as a feature extractor. The ELM unit works as the image classifier, which makes the perfect symmetry for handwritten digit recognition. A deeplearning4j (DL4J) framework-based CNN-ELM model was developed and trained using the Modified National Institute of Standards and Technology (MNIST) database. Validation of the model was performed through self-build handwritten digits and USPS test datasets. Furthermore, we observed the variation of accuracies by adding various hidden layers in the architecture. Results reveal that the CNN-ELM-DL4J approach outperforms the conventional CNN models in terms of accuracy and computational time. Full article

(This article belongs to the Section Computer)

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18 pages, 398 KiB

Open AccessArticle

An Anisotropic Model for the Universe

by Morgan Le Delliou, Maksym Deliyergiyev and Antonino del Popolo

Symmetry 2020, 12(10), 1741; https://doi.org/10.3390/sym12101741 - 21 Oct 2020

Cited by 6 | Viewed by 2062

Abstract

Motivated by the back-reaction debate, and some unexplained characteristics of the CMB, we investigate the possibility of some anisotropy in the universe observed around us. To this aim, we build up a novel prediction for the Hubble law for the late universe from [...] Read more.

Motivated by the back-reaction debate, and some unexplained characteristics of the CMB, we investigate the possibility of some anisotropy in the universe observed around us. To this aim, we build up a novel prediction for the Hubble law for the late universe from a Bianchi type I model, taken as proof of concept, transcribing the departure of such model from a ΛCDM model. We dicussed the redshift measurement in this universe, and finally formalized the Hubble diagram. Full article

(This article belongs to the Special Issue New Advances of Cosmology and Astrophysics)

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19 pages, 1004 KiB

Open AccessArticle

On Construction of Solutions of Linear Differential Systems with Argument Deviations of Mixed Type

by András Rontó and Natálie Rontóová

Symmetry 2020, 12(10), 1740; https://doi.org/10.3390/sym12101740 - 21 Oct 2020

Cited by 1 | Viewed by 1455

Abstract

We show the use of parametrization techniques and successive approximations for the effective construction of solutions of linear boundary value problems for differential systems with multiple argument deviations. The approach is illustrated with a numerical example. Full article

(This article belongs to the Special Issue Nonlinear Oscillations and Boundary Value Problems)

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16 pages, 2914 KiB

Open AccessArticle

Adaptation of a Cost Overrun Risk Prediction Model to the Type of Construction Facility

by Edyta Plebankiewicz and Damian Wieczorek

Symmetry 2020, 12(10), 1739; https://doi.org/10.3390/sym12101739 - 20 Oct 2020

Cited by 13 | Viewed by 2357

Abstract

To assess the risk of project cost overrun, it is necessary to consider large amounts of symmetric and asymmetric data. This paper proposes a cost overrun risk prediction model, the structure of which is based on the fuzzy inference model of Mamdani. The [...] Read more.

To assess the risk of project cost overrun, it is necessary to consider large amounts of symmetric and asymmetric data. This paper proposes a cost overrun risk prediction model, the structure of which is based on the fuzzy inference model of Mamdani. The model consists of numerous inputs and one output (multi-input-single-output (MISO)), based on processes running consecutively in three blocks (the fuzzy block, the interference block, and the block of sharpening the representative output value). The input variables of the model include the share of element costs in the building costs (SE), predicted changes in the number of works (WC), and expected changes in the unit price (PC). For the input variable SE, it is proposed to adjust the fuzzy set shapes to the type of building object. Single-family residential buildings, multi-family residential buildings, office buildings, highways, expressways, and sports fields were analyzed. The initial variable is the value of the risk of exceeding the costs of a given element of a construction investment project (R). In all, 27 rules were assumed in the interference block. Considering the possibility of applying sharpening methods in the cost overrun risk prediction model, the following defuzzification methods were investigated: the first of maxima, middle of maxima, and last of maxima method, the center of gravity method, and the bisector area method. Considering the advantages and disadvantages, the authors assumed that the correct and basic defuzzification method in the cost overrun risk prediction model was the center of gravity method. In order to check the correctness of the assumption made at the stage of designing the rule database, result diagrams were generated for the relationships between the variable (R) and the input variables of individual types of buildings. The results obtained confirm the correctness of the assumed assumptions and allow to consider the input variable (SE), adjusted individually to the model for each type of construction object, as crucial in the context of the impact on the output value of the output variable (R). Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models)

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16 pages, 711 KiB

Open AccessArticle

Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

by Selvi Mardalena, Purhadi Purhadi, Jerry Dwi Trijoyo Purnomo and Dedy Dwi Prastyo

Symmetry 2020, 12(10), 1738; https://doi.org/10.3390/sym12101738 - 20 Oct 2020

Cited by 10 | Viewed by 2427

Abstract

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the [...] Read more.

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors. Full article

(This article belongs to the Section Mathematics)

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18 pages, 856 KiB

Open AccessArticle

Nested Polyhedra and Indices of Orbits of Coxeter Groups of Non-Crystallographic Type

by Mariia Myronova, Jiří Patera and Marzena Szajewska

Symmetry 2020, 12(10), 1737; https://doi.org/10.3390/sym12101737 - 20 Oct 2020

Cited by 1 | Viewed by 2235

Abstract

The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallographic finite reflection groups

H_{2}

,

H_{3}

and

H_{4}

. Using a representation-orbit replacement, the definitions and [...] Read more.

The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallographic finite reflection groups

H_{2}

,

H_{3}

and

H_{4}

. Using a representation-orbit replacement, the definitions and properties of the indices are formulated for individual orbits of the examined groups. The indices of orders two and four of the tensor product of k orbits are determined. Using the branching rules for the non-crystallographic Coxeter groups, the embedding index is defined similarly to the Dynkin index of a representation. Moreover, since the definition of the indices can be applied to any orbit of non-crystallographic type, the algorithm allowing to search for the orbits of smaller radii contained within any considered one is presented for the Coxeter groups

H_{2}

and

H_{3}

. The geometrical structures of nested polytopes are exemplified. Full article

(This article belongs to the Special Issue Symmetry in Discrete and Combinatorial Geometry)

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15 pages, 315 KiB

Open AccessArticle

Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction

by Paweł Zaprawa and Katarzyna Tra̧bka-Wiȩcław

Symmetry 2020, 12(10), 1736; https://doi.org/10.3390/sym12101736 - 20 Oct 2020

Viewed by 1399

Abstract

Let

C_{0} (h)

be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula

R e {(1 - z^{2}) f^{'} (z)} > 0

. In this [...] Read more.

Let

C_{0} (h)

be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula

R e {(1 - z^{2}) f^{'} (z)} > 0

. In this paper, some coefficient problems for

C_{0} (h)

are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated. Full article

(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)

16 pages, 318 KiB

Open AccessArticle

The Fourth Axiom of Similarity Measures

by Chun-Hsiao Chu, Chih-Ping Yen and Yi-Fong Lin

Symmetry 2020, 12(10), 1735; https://doi.org/10.3390/sym12101735 - 20 Oct 2020

Cited by 4 | Viewed by 1461

Abstract

In this research, the fourth axiom to improve the well-defined examination of similarity measures is studied, where the measures have a symmetric structure. We first provide a theoretic enhancement of three correlation coefficient similarity measures that were proposed by a source paper. Second, [...] Read more.

In this research, the fourth axiom to improve the well-defined examination of similarity measures is studied, where the measures have a symmetric structure. We first provide a theoretic enhancement of three correlation coefficient similarity measures that were proposed by a source paper. Second, we use the same numerical example proposed by the source paper for pattern recognition problems to illustrate that the weighted correlation coefficient similarity measure is dependent on the set of weights. Finally, we demonstrate that the correlation coefficient similarity measure in the intuitionistic fuzzy set environment can address the issue of practical fault diagnosis when solving the turbine engine problems using similarity measures with symmetric characteristics. Full article

(This article belongs to the Section Mathematics)

23 pages, 6763 KiB

Open AccessArticle

Lorentz Violation at the Level of Undergraduate Classical Mechanics

by Madeline Clyburn and Charles D. Lane

Symmetry 2020, 12(10), 1734; https://doi.org/10.3390/sym12101734 - 20 Oct 2020

Cited by 4 | Viewed by 2316

Abstract

In this paper, we use the classical limit of the Standard-Model Extension to explore some generic features of Lorentz violation. This classical limit is formulated at the level of undergraduate physics. We first discuss the general equations of motion and then concentrate on [...] Read more.

In this paper, we use the classical limit of the Standard-Model Extension to explore some generic features of Lorentz violation. This classical limit is formulated at the level of undergraduate physics. We first discuss the general equations of motion and then concentrate on three specific systems. First, we consider the theoretical aspects of pendulum motion in the presence of Lorentz violation, followed by some sample experimental results. The experimental bounds we achieve, in the range of

10^{- 3}

, are not competitive with the current bounds from atomic clocks; rather, our experiment illustrates some common ideas and methods that appear in Lorentz-violation studies. We then discuss how Newton’s 2nd Law must be treated with caution in our model. Finally, we introduce a computational simulation of a binary star system that is perturbed by Lorentz-violating effects. This simulation shows some interesting behavior that could be the subject of future analytical studies. Full article

(This article belongs to the Section Physics)

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25 pages, 7623 KiB

Open AccessArticle

Influence of Loose Contact between Tunnel Lining and Surrounding Rock on the Safety of the Tunnel Structure

by Zijian Ye and Chengping Zhang

Symmetry 2020, 12(10), 1733; https://doi.org/10.3390/sym12101733 - 20 Oct 2020

Cited by 8 | Viewed by 2162

Abstract

The improvement of the contact state between the surrounding rock and tunnel lining, such as the effect of back-fill grouting behind lining, was important for maintaining the stability of the lining structure. To explore the influence of loose contact states behind lining on [...] Read more.

The improvement of the contact state between the surrounding rock and tunnel lining, such as the effect of back-fill grouting behind lining, was important for maintaining the stability of the lining structure. To explore the influence of loose contact states behind lining on the safety of tunnel lining, a case of field investigation in a railway tunnel with a symmetrical lining structure was presented in this paper. A model test was conducted to prove the accuracy of the numerical simulation in the condition of dense contact state between the lining and surrounding rocks. Based on this, the three-dimensional (3-D) impact of loose contact states on the mechanic behavior of the lining structure under different compactness and different loose contact areas behind lining was investigated and summarized. Furthermore, the influence of the percentage of the insufficient strength behind lining was explored. Finally, the grade of the influence of the loose contact state on the safety of the lining structure was classified. The results revealed that: (1) in order to maintain the stability of lining structure, the compactness of the back-fill grouting behind lining was recommended to be above 80%, and the range of the loose contact area should be no more than 60 degree; (2) the strength of the back-fill grouting behind lining should be above 50% strength of the surrounding rock, the loose contact state behind lining should be improved in time to avoid expansion of the loose contact area; and (3) the classification of the influence grade on the safety of the lining structure provides a basic reference for controlling the quality of the back-fill grouting. This research gives a new point of view for the evaluation of the contact state between lining and surrounding rock. Full article

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14 pages, 471 KiB

Open AccessArticle

Gradient Iterative Method with Optimal Convergent Factor for Solving a Generalized Sylvester Matrix Equation with Applications to Diffusion Equations

by Nunthakarn Boonruangkan and Pattrawut Chansangiam

Symmetry 2020, 12(10), 1732; https://doi.org/10.3390/sym12101732 - 20 Oct 2020

Cited by 2 | Viewed by 1493

Abstract

We introduce a gradient iterative scheme with an optimal convergent factor for solving a generalized Sylvester matrix equation

\sum_{i = 1}^{p} A_{i} X B_{i} = F

, where

A_{i}, B_{i}

and F are conformable rectangular matrices. [...] Read more.

We introduce a gradient iterative scheme with an optimal convergent factor for solving a generalized Sylvester matrix equation

\sum_{i = 1}^{p} A_{i} X B_{i} = F

, where

A_{i}, B_{i}

and F are conformable rectangular matrices. The iterative scheme is derived from the gradients of the squared norm-errors of the associated subsystems for the equation. The convergence analysis reveals that the sequence of approximated solutions converge to the exact solution for any initial value if and only if the convergent factor is chosen properly in terms of the spectral radius of the associated iteration matrix. We also discuss the convergent rate and error estimations. Moreover, we determine the fastest convergent factor so that the associated iteration matrix has the smallest spectral radius. Furthermore, we provide numerical examples to illustrate the capability and efficiency of this method. Finally, we apply the proposed scheme to discretized equations for boundary value problems involving convection and diffusion. Full article

(This article belongs to the Special Issue Recent Advances and Application of Iterative Methods)

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11 pages, 250 KiB

Open AccessArticle

On Optimization Techniques for the Construction of an Exponential Estimate for Delayed Recurrent Neural Networks

by Vasyl Martsenyuk, Stanislaw Rajba and Mikolaj Karpinski

Symmetry 2020, 12(10), 1731; https://doi.org/10.3390/sym12101731 - 20 Oct 2020

Cited by 1 | Viewed by 1510

Abstract

This work is devoted to the modeling and investigation of the architecture design for the delayed recurrent neural network, based on the delayed differential equations. The usage of discrete and distributed delays makes it possible to model the calculation of the next states [...] Read more.

This work is devoted to the modeling and investigation of the architecture design for the delayed recurrent neural network, based on the delayed differential equations. The usage of discrete and distributed delays makes it possible to model the calculation of the next states using internal memory, which corresponds to the artificial recurrent neural network architecture used in the field of deep learning. The problem of exponential stability of the models of recurrent neural networks with multiple discrete and distributed delays is considered. For this purpose, the direct method of stability research and the gradient descent method is used. The methods are used consequentially. Firstly we use the direct method in order to construct stability conditions (resulting in an exponential estimate), which include the tuple of positive definite matrices. Then we apply the optimization technique for these stability conditions (or of exponential estimate) with the help of a generalized gradient method with respect to this tuple of matrices. The exponential estimates are constructed on the basis of the Lyapunov–Krasovskii functional. An optimization method of improving estimates is offered, which is based on the notion of the generalized gradient of the convex function of the tuple of positive definite matrices. The search for the optimal exponential estimate is reduced to finding the saddle point of the Lagrange function. Full article

(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications)

16 pages, 376 KiB

Open AccessArticle

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

by Samad Noeiaghdam, Aliona Dreglea, Jihuan He, Zakieh Avazzadeh, Muhammad Suleman, Mohammad Ali Fariborzi Araghi, Denis N. Sidorov and Nikolai Sidorov

Symmetry 2020, 12(10), 1730; https://doi.org/10.3390/sym12101730 - 20 Oct 2020

Cited by 35 | Viewed by 2658

Abstract

This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the [...] Read more.

This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method. Full article

(This article belongs to the Special Issue Integral Equations: Theories, Approximations and Applications)

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15 pages, 825 KiB

Open AccessArticle

Attention-Based LSTM with Filter Mechanism for Entity Relation Classification

by Yanliang Jin, Dijia Wu and Weisi Guo

Symmetry 2020, 12(10), 1729; https://doi.org/10.3390/sym12101729 - 19 Oct 2020

Cited by 15 | Viewed by 3892

Abstract

Relation classification is an important research area in the field of natural language processing (NLP), which aims to recognize the relationship between two tagged entities in a sentence. The noise caused by irrelevant words and the word distance between the tagged entities may [...] Read more.

Relation classification is an important research area in the field of natural language processing (NLP), which aims to recognize the relationship between two tagged entities in a sentence. The noise caused by irrelevant words and the word distance between the tagged entities may affect the relation classification accuracy. In this paper, we present a novel model multi-head attention long short term memory (LSTM) network with filter mechanism (MALNet) to extract the text features and classify the relation of two entities in a sentence. In particular, we combine LSTM with attention mechanism to obtain the shallow local information and introduce a filter layer based on attention mechanism to strength the available information. Besides, we design a semantic rule for marking the key word between the target words and construct a key word layer to extract its semantic information. We evaluated the performance of our model on SemEval-2010 Task8 dataset and KBP-37 dataset. We achieved an F1-score of 86.3% on SemEval-2010 Task8 dataset and F1-score of 61.4% on KBP-37 dataset, which shows that our method is superior to the previous state-of-the-art methods. Full article

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10 pages, 283 KiB

Open AccessArticle

Optimal and Nonoptimal Gronwall Lemmas

by Daniela Marian, Sorina Anamaria Ciplea and Nicolaie Lungu

Symmetry 2020, 12(10), 1728; https://doi.org/10.3390/sym12101728 - 19 Oct 2020

Cited by 3 | Viewed by 1258

Abstract

In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. [...] Read more.

In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one. Full article

(This article belongs to the Section Mathematics)

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17 pages, 3590 KiB

Open AccessArticle

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

by Susmita Das, Dalia Nandi, Biswarup Neogi and Biswajit Sarkar

Symmetry 2020, 12(10), 1727; https://doi.org/10.3390/sym12101727 - 19 Oct 2020

Cited by 3 | Viewed by 2148

Abstract

System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design [...] Read more.

System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design is the focus of the present work. Different postures of lower limb have been considered in this paper to be analyzed for artificial system design of lower limb movement. The generated polynomial equations of the sitting and standing positions of the normal limb are represented with overall system transfer function. The behavioral analysis of the lower limb model shows the nonlinear nature. The Euler-Lagrange method is utilized to describe the nonlinearity in the field of forward dynamics of the artificial system. The stability factor through phase portrait analysis is checked with respect to nonlinear system characteristics of the lower limb. The asymptotic stability has been achieved utilizing the most applicable Lyapunov method for nonlinear systems. The stability checking of the proposed artificial lower extremity is the newer approach needed to take decisions on output implementation in the system design. Full article

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13 pages, 3476 KiB

Open AccessReview

Photochemical Methods for the Real-Time Observation of Phase Transition Processes upon Crystallization

by Fuyuki Ito

Symmetry 2020, 12(10), 1726; https://doi.org/10.3390/sym12101726 - 19 Oct 2020

Cited by 4 | Viewed by 1991

Abstract

We have used the fluorescence detection of phase transformation dynamics of organic compounds by photochemical methods to observe a real-time symmetry breaking process. The organic fluorescent molecules vary the fluorescence spectra depending on molecular aggregated states, implying fluorescence spectroscopy can be applied to [...] Read more.

We have used the fluorescence detection of phase transformation dynamics of organic compounds by photochemical methods to observe a real-time symmetry breaking process. The organic fluorescent molecules vary the fluorescence spectra depending on molecular aggregated states, implying fluorescence spectroscopy can be applied to probe the evolution of the molecular-assembling process. As an example, the amorphous-to-crystal phase transformation and crystallization with symmetry breaking at droplet during the solvent evaporation of mechanofluorochromic molecules are represented in this review. Full article

(This article belongs to the Special Issue Chemical Symmetry Breaking)

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Graphical abstract

23 pages, 12149 KiB

Open AccessArticle

Vacant Parking Slot Recognition Method for Practical Autonomous Valet Parking System Using around View Image

by Seunghyun Kim, Joongsik Kim, Moonsoo Ra and Whoi-Yul Kim

Symmetry 2020, 12(10), 1725; https://doi.org/10.3390/sym12101725 - 19 Oct 2020

Cited by 8 | Viewed by 4892

Abstract

The parking assist system (PAS) provides information of parking slots around the vehicle. As the demand for an autonomous system is increasing, intelligent PAS has been developed to park the vehicle without the driver’s intervention. To locate parking slots, most existing methods detect [...] Read more.

The parking assist system (PAS) provides information of parking slots around the vehicle. As the demand for an autonomous system is increasing, intelligent PAS has been developed to park the vehicle without the driver’s intervention. To locate parking slots, most existing methods detect slot markings on the ground using an around-view monitoring (AVM) image. There are many types of parking slots of different shapes in the real world. Due to this fact, these methods either limit their target types or use predefined slot information of different types to cover the types. However, the approach using predefined slot information cannot handle more complex cases where the slot markings are connected to other line markings and the angle between slot marking is slightly different from the predefined settings. To overcome this problem, we propose a method to detect parking slots of various shapes without predefined type information. The proposed method is the first to introduce a free junction type feature to represent the structure of parking slot junction. Since the parking slot has a modular or repeated junction pattern at both sides, junction pair consisting of one parking slot can be detected using the free junction type feature. In this process, the geometrically symmetric characteristic of the junction pair is crucial to find each junction pair. The entrance of parking slot is reconstructed according to the structure of junction pair. Then, the vacancy of the parking slot is determined by a support vector machine. The Kalman tracker is applied for each detected parking slot to ensure stability of the detection in consecutive frames. We evaluate the performance of the proposed method by using manually collected datasets, captured in different parking environments. The experimental results show that the proposed method successfully detects various types of parking slots without predefined slot type information in different environments. Full article

(This article belongs to the Special Issue Symmetry in Computer Vision and Its Applications)

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20 pages, 320 KiB

Open AccessArticle

Subordination and Superordination Properties for Certain Family of Analytic Functions Associated with Mittag–Leffler Function

by Mansour F. Yassen, Adel A. Attiya and Praveen Agarwal

Symmetry 2020, 12(10), 1724; https://doi.org/10.3390/sym12101724 - 19 Oct 2020

Cited by 22 | Viewed by 1936

Abstract

We obtain new outcomes of analytic functions linked with operator

H_{α, β}^{η, k} (f)

defined by Mittag–Leffler function. Moreover, new theorems of differential sandwich-type are obtained. Full article

(This article belongs to the Special Issue Advanced Calculus in Problems with Symmetry)

19 pages, 3109 KiB

Open AccessArticle

A Comparative Usability Study of Bare Hand Three-Dimensional Object Selection Techniques in Virtual Environment

by Xiaozhou Zhou, Hao Qin, Weiye Xiao, Lesong Jia and Chengqi Xue

Symmetry 2020, 12(10), 1723; https://doi.org/10.3390/sym12101723 - 19 Oct 2020

Cited by 5 | Viewed by 2234

Abstract

Object selection is the basis of natural user–computer interaction (NUI) in a virtual environment (VE). Among the three-dimensional object selection techniques employed in virtual reality (VR), bare hand-based finger clicking interaction and ray-casting are two convenient approaches with a high level of acceptance. [...] Read more.

Object selection is the basis of natural user–computer interaction (NUI) in a virtual environment (VE). Among the three-dimensional object selection techniques employed in virtual reality (VR), bare hand-based finger clicking interaction and ray-casting are two convenient approaches with a high level of acceptance. This study involved 14 participants, constructed a virtual laboratory environment in VR, and compared the above two finger-based interaction techniques in terms of aspects of the task performance, including the success rate, total reaction time, operational deviation, and accuracy, at different spatial positions. The results indicated that the applicable distance range of finger clicking interaction and finger ray-casting was 0.2 to 1.4 m and over 0.4 m, respectively. Within the shared applicable distance, the finger clicking interaction achieved a shorter total reaction time and higher clicking accuracy. The performance of finger clicking interaction varied remarkably at the center and edge of the horizontal field of view, while no significant difference was found among ray-casting at various horizontal azimuths. The current findings could be directly applied to the application of bare-hand interaction in VR environments. Full article

(This article belongs to the Section Computer)

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22 pages, 8428 KiB

Open AccessArticle

Optimal Design of Virtual Reality Visualization Interface Based on Kansei Engineering Image Space Research

by Qianwen Fu, Jian Lv, Shihao Tang and Qingsheng Xie

Symmetry 2020, 12(10), 1722; https://doi.org/10.3390/sym12101722 - 19 Oct 2020

Cited by 11 | Viewed by 3104

Abstract

To effectively organize design elements in virtual reality (VR) scene design and provide evaluation methods for the design process, we built a user image space cognitive model. This involved perceptual engineering methods and optimization of the VR interface. First, we studied the coupling [...] Read more.

To effectively organize design elements in virtual reality (VR) scene design and provide evaluation methods for the design process, we built a user image space cognitive model. This involved perceptual engineering methods and optimization of the VR interface. First, we studied the coupling of user cognition and design features in the VR system via the Kansei Engineering (KE) method. The quantitative theory I and KE model regression analysis were used to analyze the design elements of the VR system’s human–computer interaction interface. Combined with the complex network method, we summarized the relationship between design features and analyzed the important design features that affect users’ perceptual imagery. Then, based on the characteristics of machine learning, we used a convolutional neural network (CNN) to predict and analyze the user’s perceptual imagery in the VR system, to provide assistance for the design optimization of the VR system design. Finally, we verified the validity and feasibility of the solution by combining it with the human–machine interface design of the VR system. We conducted a feasibility analysis of the KE model, in which the similarity between the multivariate regression analysis of the VR intention space and the experimental test was approximately 97% and the error was very small; thus, the VR intention space model was well correlated. The Mean Square Error (MSE) of the convolutional neural network (CNN) prediction model was calculated with a measured value of 0.0074, and the MSE value was less than 0.01. The results show that this method can improve the effectiveness and feasibility of the design scheme. Designers use important design feature elements to assist in VR system optimization design and use CNN machine learning methods to predict user image values in VR systems and improve the design efficiency. Facing the same design task requirements in VR system interfaces, the traditional design scheme was compared with the scheme optimized by this method. The results showed that the design scheme optimized by this method better fits the user’s perceptual imagery index, and thus the user’s task operation experience was better. Full article

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29 pages, 376 KiB

Open AccessArticle

A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric

by Martin Land

Symmetry 2020, 12(10), 1721; https://doi.org/10.3390/sym12101721 - 19 Oct 2020

Cited by 7 | Viewed by 1547

Abstract

We propose a field theory for the local metric in Stueckelberg–Horwitz–Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines

x^{μ} (τ)

(

μ = 0, 1, 2, 3

) is parameterized by an [...] Read more.

We propose a field theory for the local metric in Stueckelberg–Horwitz–Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines

x^{μ} (τ)

(

μ = 0, 1, 2, 3

) is parameterized by an external time

τ

. Combining insights from SHP electrodynamics and the ADM formalism in general relativity, we generalize the notion of a 4D spacetime

M

to a formal manifold

M_{5} = M \times R

, representing an admixture of geometry (the diffeomorphism invariance of

M

) and dynamics (the system evolution of

M (τ)

with the monotonic advance of

τ \in R

). Strategically breaking the formal 5D symmetry of a metric

g_{α β} (x, τ)

(

α, β = 0, 1, 2, 3, 5

) posed on

M_{5}

, we obtain ten unconstrained Einstein equations for the

τ

-evolution of the 4D metric

γ_{μ ν} (x, τ)

and five constraints that are to be satisfied by the initial conditions. The resulting theory differs from five-dimensional (5D) gravitation, much as SHP U(1) gauge theory differs from 5D electrodynamics. Full article

(This article belongs to the Special Issue New Advances of Cosmology and Astrophysics)

22 pages, 9092 KiB

Open AccessArticle

From Probabilistic to Quantile-Oriented Sensitivity Analysis: New Indices of Design Quantiles

by Zdeněk Kala

Symmetry 2020, 12(10), 1720; https://doi.org/10.3390/sym12101720 - 19 Oct 2020

Cited by 16 | Viewed by 7627

Abstract

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability P_f of a structure. Although the reliability is usually expressed via P_f, Eurocode building design standards assess the reliability using [...] Read more.

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability P_f of a structure. Although the reliability is usually expressed via P_f, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as P_f-oriented SA or local SA based on P_f derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for P_f ranging from 9.35 × 10⁻⁸ to 1–1.51 × 10⁻⁸. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small P_f. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article. Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models)

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21 pages, 532 KiB

Open AccessArticle

Algebraic DVR Approaches Applied to Describe the Stark Effect

by Marisol Bermúdez-Montaña, Marisol Rodríguez-Arcos, Renato Lemus, José M. Arias, Joaquín Gómez-Camacho and Emilio Orgaz

Symmetry 2020, 12(10), 1719; https://doi.org/10.3390/sym12101719 - 19 Oct 2020

Cited by 7 | Viewed by 2217

Abstract

Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the [...] Read more.

Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators

r^{2}

and

p^{2}

are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the

U (4)

dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers

n = 2, 3

with

m = 0

. Full article

(This article belongs to the Special Issue Symmetries in Quantum Mechanics)

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