Symmetry

16 pages, 3611 KiB

Open AccessArticle

Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection

by Qiubao Wang, Xing Zhang and Yuejuan Yang

Symmetry 2019, 11(11), 1428; https://doi.org/10.3390/sym11111428 - 19 Nov 2019

Cited by 5 | Viewed by 2433

Abstract

This paper presents the dynamic behaviors of a second-order asymmetric stochastic delay system with a Duffing oscillator as well as through the detection of weak signals, which are analyzed theoretically and numerically. The dynamic behaviors of the asymmetric system are analyzed based on [...] Read more.

This paper presents the dynamic behaviors of a second-order asymmetric stochastic delay system with a Duffing oscillator as well as through the detection of weak signals, which are analyzed theoretically and numerically. The dynamic behaviors of the asymmetric system are analyzed based on the stochastic center manifold, together with Hopf bifurcation. Numerical analysis revealed that the time delay could enhance the noise immunity of the asymmetric system so as to enhance the asymmetric system’s ability to detect weak signals. The frequency of the weak signal under noise excitation was detected through the ‘act-and-wait’ method. The small amplitude was detected through the transition from the chaotic to the periodic state. Theoretical analysis and numerical simulation indicate that the application of the asymmetric Duffing oscillator with delay to detect weak signal is feasible. Full article

► Show Figures

Figure 1

12 pages, 274 KiB

Open AccessArticle

A Conformally Invariant Derivation of Average Electromagnetic Helicity

by Ivan Fernandez-Corbaton

Symmetry 2019, 11(11), 1427; https://doi.org/10.3390/sym11111427 - 19 Nov 2019

Cited by 5 | Viewed by 2919

Abstract

The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in [...] Read more.

The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in

(r, t)

space, and in the time-harmonic

(r, ω)

space are obtained, featuring Riemann–Silberstein-like fields and potentials. The time-harmonic expressions can be directly evaluated using the outputs of common numerical solvers of Maxwell equations. The results are shown to be equivalent to the well-known volume integral for the average helicity, featuring the electric and magnetic fields and potentials. Full article

(This article belongs to the Special Issue Duality Symmetry)

24 pages, 4183 KiB

Open AccessArticle

A Decision Support System Using Text Mining Based Grey Relational Method for the Evaluation of Written Exams

by Mehmet Erkan Yuksel and Huseyin Fidan

Symmetry 2019, 11(11), 1426; https://doi.org/10.3390/sym11111426 - 19 Nov 2019

Cited by 6 | Viewed by 3723

Abstract

Grey relational analysis (GRA) is a part of the Grey system theory (GST). It is appropriate for solving problems with complicated interrelationships between multiple factors/parameters and variables. It solves multiple-criteria decision-making problems by combining the entire range of performance attribute values being considered [...] Read more.

Grey relational analysis (GRA) is a part of the Grey system theory (GST). It is appropriate for solving problems with complicated interrelationships between multiple factors/parameters and variables. It solves multiple-criteria decision-making problems by combining the entire range of performance attribute values being considered for every alternative into one single value. Thus, the main problem is reduced to a single-objective decision-making problem. In this study, we developed a decision support system for the evaluation of written exams with the help of GRA using contextual text mining techniques. The answers obtained from the written exam with the participation of 50 students in a computer laboratory and the answer key prepared by the instructor constituted the data set of the study. A symmetrical perspective allows us to perform relational analysis between the students’ answers and the instructor’s answer key in order to contribute to the measurement and evaluation. Text mining methods and GRA were applied to the data set through the decision support system employing the SQL Server database management system, C#, and Java programming languages. According to the results, we demonstrated that the exam papers are successfully ranked and graded based on the word similarities in the answer key. Full article

► Show Figures

Figure 1

12 pages, 3396 KiB

Open AccessArticle

Statistic-Driven Proton Transfer Affecting Nanoscopic Organization in an Ethylammonium Nitrate Ionic Liquid and 1,4-Diaminobutane Binary Mixture: A Steamy Pizza Model

by Alessandro Mariani, Matteo Bonomo and Stefano Passerini

Symmetry 2019, 11(11), 1425; https://doi.org/10.3390/sym11111425 - 19 Nov 2019

Cited by 6 | Viewed by 3312

Abstract

Herein, we report on the theoretical and experimental investigation of the chemical equilibrium in a Ethylammonium Nitrate (EAN)/1,4-Diaminobutane (DAB) binary mixture displaying a significant excess of the latter component (namely, a 1:9 mole ratio). Both the neutral compounds, i.e., ethylamine (EtNH₂) [...] Read more.

Herein, we report on the theoretical and experimental investigation of the chemical equilibrium in a Ethylammonium Nitrate (EAN)/1,4-Diaminobutane (DAB) binary mixture displaying a significant excess of the latter component (namely, a 1:9 mole ratio). Both the neutral compounds, i.e., ethylamine (EtNH₂) and DAB, present very similar chemical properties, especially concerning their basic strength, resulting in a continuous jump of the proton from the ethylammonium to the diamine (and vice-versa). Due to the significant excess of DAB, the proton is (statistically) expected to be bound to one of its nitrogen atoms, leading to the formation of a new (ternary) mixture containing DAB (ca. 80%), ethylamine (ca. 10%) and 4-amino-1-butylammonium nitrate (ABAN, ca. 10%). This is probed by means of SAXS measurements, showing LqE (low q excess) that increases over time. This feature tends to stabilize after approximately one day. When the measurement is repeated after one year, the LqE feature shows an increased intensity. Based on the results of our simulations, we suggest that this phenomenon is likely due to partial ethylamine evaporation, pushing the equilibrium toward the formation of ABAN. Full article

(This article belongs to the Special Issue Materials Science and X-Ray Diffraction)

► Show Figures

Graphical abstract

18 pages, 4227 KiB

Open AccessArticle

Robust Hybrid Beamforming Scheme for Millimeter-Wave Massive-MIMO 5G Wireless Networks

by Saleem Latteef Mohammed, Mohammed H. Alsharif, Sadik Kamel Gharghan, Imran Khan and Mahmoud Albreem

Symmetry 2019, 11(11), 1424; https://doi.org/10.3390/sym11111424 - 18 Nov 2019

Cited by 47 | Viewed by 4933

Abstract

Wireless networks employing millimeter-wave (mmWave) and Massive Multiple-Input Multiple-Output (MIMO) technologies are a key approach to boost network capacity, coverage, and quality of service (QoS) for future communications. They deploy symmetric antennas on a large scale in order to enhance the system throughput [...] Read more.

Wireless networks employing millimeter-wave (mmWave) and Massive Multiple-Input Multiple-Output (MIMO) technologies are a key approach to boost network capacity, coverage, and quality of service (QoS) for future communications. They deploy symmetric antennas on a large scale in order to enhance the system throughput and data rate. However, increasing the number of antennas and Radio Frequency (RF) chains results in high computational complexity and more energy requirements. Therefore, to solve these problems, this paper proposes a low-complexity hybrid beamforming scheme for mmWave Massive-MIMO 5G wireless networks. The proposed algorithm is on the basis of alternating the minimum mean square error (Alt-MMSE) hybrid beamforming technique in which the orthogonal properties of the digital matrix were designed, and then the MSE of the transmitted and received signal was reduced. The phase of the analog matrix was obtained from the updated digital matrix. Simulation results showed that the proposed hybrid beamforming algorithm had better performance than existing state-of-the-art algorithms, and similar performance with the optimal digital precoding algorithm. Full article

(This article belongs to the Special Issue Information Technologies and Electronics)

► Show Figures

Figure 1

16 pages, 908 KiB

Open AccessArticle

Feature Selection Based on Swallow Swarm Optimization for Fuzzy Classification

by Ilya Hodashinsky, Konstantin Sarin, Alexander Shelupanov and Artem Slezkin

Symmetry 2019, 11(11), 1423; https://doi.org/10.3390/sym11111423 - 18 Nov 2019

Cited by 16 | Viewed by 3120

Abstract

This paper concerns several important topics of the Symmetry journal, namely, pattern recognition, computer-aided design, diversity and similarity. We also take advantage of the symmetric structure of a membership function. Searching for the (sub) optimal subset of features is an NP-hard problem. In [...] Read more.

This paper concerns several important topics of the Symmetry journal, namely, pattern recognition, computer-aided design, diversity and similarity. We also take advantage of the symmetric structure of a membership function. Searching for the (sub) optimal subset of features is an NP-hard problem. In this paper, a binary swallow swarm optimization (BSSO) algorithm for feature selection is proposed. To solve the classification problem, we use a fuzzy rule-based classifier. To evaluate the feature selection performance of our method, BSSO is compared to induction without feature selection and some similar algorithms on well-known benchmark datasets. Experimental results show the promising behavior of the proposed method in the optimal selection of features. Full article

(This article belongs to the Special Issue Information Technologies and Electronics)

► Show Figures

Figure 1

15 pages, 2252 KiB

Open AccessArticle

Makeup Interpolation Based on Color and Shape Parametrization

by Jieun Cho, Jun Ohya and Sang Il Park

Symmetry 2019, 11(11), 1422; https://doi.org/10.3390/sym11111422 - 18 Nov 2019

Cited by 4 | Viewed by 3406

Abstract

In this paper, we address the problem of synthesizing continuous variations with the appearance of makeup by taking a linear combination of the examples. Makeup usually shows a vague boundary and does not form a clear shape, which makes this problem unique from [...] Read more.

In this paper, we address the problem of synthesizing continuous variations with the appearance of makeup by taking a linear combination of the examples. Makeup usually shows a vague boundary and does not form a clear shape, which makes this problem unique from the existing image interpolation problems. We approach this problem as an interpolation between semi-transparent image layers and tackle this by presenting new parametrization schemes for the color and for the shape separately in order to achieve an effective interpolation. For the color parametrization, our main idea is based on the observation of the symmetric relation between the color and transparency of the makeup; we provide an optimization framework for extracting a representative palette of colors associated with the transparent values, which enables us to easily set up the color correspondence among the multiple makeup samples. For the shape parametrization, we exploit a polar coordinate system, that creates the in-between shapes effectively, without ghosting artifacts. Full article

► Show Figures

Figure 1

21 pages, 833 KiB

Open AccessArticle

Agglomeration Economies: An Analysis of the Determinants of Employment in the Cities of Ecuador

by Tania Paola Torres-Gutiérrez, Ronny Correa-Quezada, José Álvarez-García and María de la Cruz del Río-Rama

Symmetry 2019, 11(11), 1421; https://doi.org/10.3390/sym11111421 - 16 Nov 2019

Cited by 5 | Viewed by 4338

Abstract

The objective of this investigation is to study the role of agglomeration economies (manufacturing) in urban employment growth, as a proxy for economic growth, between 1980 and 2010 in Ecuador. The three measures of agglomeration-specialization, diversity, and density-are tested to determine their effect [...] Read more.

The objective of this investigation is to study the role of agglomeration economies (manufacturing) in urban employment growth, as a proxy for economic growth, between 1980 and 2010 in Ecuador. The three measures of agglomeration-specialization, diversity, and density-are tested to determine their effect on employment growth in industries. The empirical analysis is based on firm- and city-level data from manufacturing activities. A model is proposed to estimate the effect of agglomeration economies on the growth of employment and a regression is conducted using instrumental variables. In particular, the two-stage least squares (2SLS) estimator is used. We conclude that localization economies measured by a specialization index have a positive impact on the growth of employment in the period analyzed. The results are similar to those obtained by other work carried out both in developed and developing countries. Full article

► Show Figures

Figure 1

12 pages, 2402 KiB

Open AccessArticle

Closed Form Solutions for Nonlinear Oscillators Under Discontinuous and Impulsive Periodic Excitations

by Valery Pilipchuk

Symmetry 2019, 11(11), 1420; https://doi.org/10.3390/sym11111420 - 16 Nov 2019

Cited by 1 | Viewed by 2359

Abstract

Periodic responses of linear and nonlinear systems under discontinuous and impulsive excitations are analyzed with non-smooth temporal transformations incorporating temporal symmetries of periodic processes. The related analytical manipulations are illustrated on a strongly nonlinear oscillator whose free vibrations admit an exact description in [...] Read more.

Periodic responses of linear and nonlinear systems under discontinuous and impulsive excitations are analyzed with non-smooth temporal transformations incorporating temporal symmetries of periodic processes. The related analytical manipulations are illustrated on a strongly nonlinear oscillator whose free vibrations admit an exact description in terms of elementary functions. As a result, closed form analytical solutions for the non-autonomous strongly nonlinear case are obtained. Conditions of existence for such solutions are represented as a family of period-amplitude curves. The family is represented by different couples of solutions associated with different numbers of vibration half cycles between any two consecutive pulses. Poincaré sections showed that the oscillator can respond quite chaotically when shifting from the period-amplitude curves. Full article

(This article belongs to the Special Issue Asymptotic Methods in the Mechanics and Nonlinear Dynamics)

► Show Figures

Figure 1

11 pages, 354 KiB

Open AccessArticle

Lorentz Violation Footprints in the Spectrum of High-Energy Cosmic Neutrinos—Deformation of the Spectrum of Superluminal Neutrinos from Electron-Positron Pair Production in Vacuum

by José Manuel Carmona, José Luis Cortés, José Javier Relancio and Maykoll Anthonny Reyes

Symmetry 2019, 11(11), 1419; https://doi.org/10.3390/sym11111419 - 16 Nov 2019

Cited by 9 | Viewed by 2718

Abstract

The observation of cosmic neutrinos up to 2 PeV is used to put bounds on the energy scale of Lorentz invariance violation through the loss of energy due to the production of

e^{+} e^{-}

pairs in the propagation of superluminal neutrinos. [...] Read more.

The observation of cosmic neutrinos up to 2 PeV is used to put bounds on the energy scale of Lorentz invariance violation through the loss of energy due to the production of

e^{+} e^{-}

pairs in the propagation of superluminal neutrinos. A model to study this effect, which allows us to understand qualitatively the results of numerical simulations, is presented. Full article

► Show Figures

Figure 1

8 pages, 328 KiB

Open AccessArticle

The Grimus–Neufeld Model with FlexibleSUSY at One-Loop

by Simonas Draukšas, Vytautas Dūdėnas, Thomas Gajdosik, Andrius Juodagalvis, Paulius Juodsnukis and Darius Jurčiukonis

Symmetry 2019, 11(11), 1418; https://doi.org/10.3390/sym11111418 - 16 Nov 2019

Viewed by 2530

Abstract

The Grimus–Neufeld model can explain the smallness of measured neutrino masses by extending the Standard Model with a single heavy neutrino and a second Higgs doublet, using the seesaw mechanism and radiative mass generation. The Grimus–Lavoura approximation allows us to calculate the light [...] Read more.

The Grimus–Neufeld model can explain the smallness of measured neutrino masses by extending the Standard Model with a single heavy neutrino and a second Higgs doublet, using the seesaw mechanism and radiative mass generation. The Grimus–Lavoura approximation allows us to calculate the light neutrino masses analytically. By inverting these analytic expressions, we determine the neutrino Yukawa couplings from the measured neutrino mass differences and the neutrino mixing matrix. Short-cutting the full renormalization of the model, we implement the Grimus–Neufeld model in the spectrum calculator FlexibleSUSY and check the consistency of the implementation. These checks hint that FlexibleSUSY is able to do the job of numerical renormalization in a restricted parameter space. As a summary, we also comment on further steps of the implementation and the use of FlexibleSUSY for the model. Full article

(This article belongs to the Special Issue Selected Papers from 43rd International Conference of Theoretical Physics: Matter to the Deepest, Recent Developments In Physics Of Fundamental Interactions (MTTD2019))

► Show Figures

Figure 1

8 pages, 257 KiB

Open AccessFeature PaperArticle

On Some Sufficient Conditions for a Function to Be p-Valent Starlike

by Mamoru Nunokawa, Janusz Sokół and Edyta Trybucka

Symmetry 2019, 11(11), 1417; https://doi.org/10.3390/sym11111417 - 15 Nov 2019

Viewed by 1735

Abstract

A function f analytic in a domain

D \in C

is called p-valent in D, if for every complex number w, the equation

f (z) = w

has at most p roots in D, so that there [...] Read more.

A function f analytic in a domain

D \in C

is called p-valent in D, if for every complex number w, the equation

f (z) = w

has at most p roots in D, so that there exists a complex number

w_{0}

such that the equation

f (z) = w_{0}

has exactly p roots in D. The aim of this paper is to establish some sufficient conditions for a function analytic in the unit disc

D

to be p-valent starlike in

D

or to be at most p-valent in

D

. Our results are proved mainly by applying Nunokawa’s lemmas. Full article

14 pages, 5658 KiB

Open AccessArticle

Study of Indoor Ventilation Based on Large-Scale DNS by a Domain Decomposition Method

by Junyang Jiang, Zichao Jiang, Trevor Hocksun Kwan, Chun-Ho Liu and Qinghe Yao

Symmetry 2019, 11(11), 1416; https://doi.org/10.3390/sym11111416 - 15 Nov 2019

Cited by 3 | Viewed by 2817

Abstract

This paper presents a large-scale Domain Decomposition Method (DDM) based Direct Numerical Simulation (DNS) for predicting the behavior of indoor airflow, where the aim is to design a comfortable and efficient indoor air environment of modern buildings. An analogy of the single-phase convection [...] Read more.

This paper presents a large-scale Domain Decomposition Method (DDM) based Direct Numerical Simulation (DNS) for predicting the behavior of indoor airflow, where the aim is to design a comfortable and efficient indoor air environment of modern buildings. An analogy of the single-phase convection problems is applied, and the pressure stabilized domain decomposition method is used to symmetrize the linear systems of Navier-Stokes equations and the convection-diffusion equation. Furthermore, a balancing preconditioned conjugate gradient method is utilized to deal with the interface problem caused by domain decomposition. The entire simulation model is validated by comparing the numerical results with that of recognized experimental and numerical data from previous literature. The transient behavior of indoor airflow and its complexity in the ventilated room are discussed; the velocity and vortex distribution of airflow are investigated, and its possible influence on particle accumulation is classified. Full article

(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)

► Show Figures

Figure 1

13 pages, 355 KiB

Open AccessArticle

An E-Sequence Approach to the 3x + 1 Problem

by Sanmin Wang

Symmetry 2019, 11(11), 1415; https://doi.org/10.3390/sym11111415 - 15 Nov 2019

Viewed by 2067

Abstract

For any odd positive integer x, define

{(x_{n})}_{n ⩾ 0}

and

{(a_{n})}_{n ⩾ 1}

by setting [...] Read more.

For any odd positive integer x, define

{(x_{n})}_{n ⩾ 0}

and

{(a_{n})}_{n ⩾ 1}

by setting

x_{0} = x, x_{n} = \frac{3 x_{n - 1} + 1}{2^{a_{n}}}

such that all

x_{n}

are odd. The

3 x + 1

problem asserts that there is an

x_{n} = 1

for all x. Usually,

{(x_{n})}_{n ⩾ 0}

is called the trajectory of x. In this paper, we concentrate on

{(a_{n})}_{n ⩾ 1}

and call it the E-sequence of x. The idea is that we generalize E-sequences to all infinite sequences

{(a_{n})}_{n ⩾ 1}

of positive integers and consider all these generalized E-sequences. We then define

{(a_{n})}_{n ⩾ 1}

to be

Ω

-convergent to x if it is the E-sequence of x and to be

Ω

-divergent if it is not the E-sequence of any odd positive integer. We prove a remarkable fact that the

Ω

-divergence of all non-periodic E-sequences implies the periodicity of

{(x_{n})}_{n ⩾ 0}

for all

x_{0}

. The principal results of this paper are to prove the

Ω

-divergence of several classes of non-periodic E-sequences. Especially, we prove that all non-periodic E-sequences

{(a_{n})}_{n ⩾ 1}

with

\underset{n \to \infty}{lim^{¯}} \frac{b_{n}}{n} > {log}_{2} 3

are

Ω

-divergent by using Wendel’s inequality and the Matthews and Watts’ formula

x_{n} = \frac{3^{n} x_{0}}{2^{b_{n}}} \prod_{k = 0}^{n - 1} (1 + \frac{1}{3 x_{k}})

, where

b_{n} = \sum_{k = 1}^{n} a_{k}

. These results present a possible way to prove the periodicity of trajectories of all positive integers in the

3 x + 1

problem, and we call it the E-sequence approach. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

16 pages, 3043 KiB

Open AccessArticle

Dynamic Soft Sensor Development for Time-Varying and Multirate Data Processes Based on Discount and Weighted ARMA Models

by Longhao Li and Yongshou Dai

Symmetry 2019, 11(11), 1414; https://doi.org/10.3390/sym11111414 - 15 Nov 2019

Cited by 3 | Viewed by 2541

Abstract

To solve the soft sensor modeling (SSMI) problem in a nonlinear chemical process with dynamic time variation and multi-rate data, this paper proposes a dynamic SSMI method based on an autoregressive moving average (ARMA) model of weighted process data with discount (DSSMI-AMWPDD) and [...] Read more.

To solve the soft sensor modeling (SSMI) problem in a nonlinear chemical process with dynamic time variation and multi-rate data, this paper proposes a dynamic SSMI method based on an autoregressive moving average (ARMA) model of weighted process data with discount (DSSMI-AMWPDD) and optimization methods. For the sustained influence of auxiliary variable data on the dominant variables, the ARMA model structure is adopted. To reduce the complexity of the model, the dynamic weighting model is combined with the ARMA model. To address the weights of auxiliary variable data with different sampling frequencies, a calculation method for AMWPDD is proposed using assumptions that are suitable for most sequential chemical processes. The proposed method can obtain a discount factor value (DFV) of auxiliary variable data, realizing the dynamic fusion of chemical process data. Particle swarm optimization (PSO) is employed to optimize the soft sensor model parameters. To address the poor convergence problem of PSO, ω-dynamic PSO (ωDPSO) is used to improve the PSO convergence via the dynamic fluctuation of the inertia weight. A continuous stirred tank reactor (CSTR) simulation experiment was performed. The results show that the proposed DSSMI-AMWPDD method can effectively improve the SSM prediction accuracy for a nonlinear time-varying chemical process. The AMWPDD proposed in this paper can reflect the dynamic change of chemical process and improve the accuracy of SSM data prediction. The ω dynamic PSO method proposed in this paper has faster convergence speed and higher convergence accuracy, thus, these models correlate with the concept of symmetry. Full article

(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)

► Show Figures

Figure 1

Figure 1
Irregular quality sample in the chemical process. Full article ">Figure 2
Multipoint input ARMA model structure. Full article ">Figure 3
Dynamic weighted ARMA model structure. Full article ">Figure 4
Discount-weighted ARMA model structure. Full article ">Figure 5
Dynamic adjustment of inertia weight ω in 100 iterations. Full article ">Figure 6
The principle of the CSTR. Full article ">Figure 7
Variation pattern of catalyst activity k0. Full article ">Figure 8
Modeling data training for the different SSMI methods. (a) The training curve based on LSSVM; (b) The training curve based on PSO-LSSVM; (c) The training curve based on ωDPSO-LSSVM. Full article ">Figure 9
Prediction of test data by the different SSMI methods. (a) The prediction curve based on LSSVM; (b) The prediction curve based on PSO-LSSVM; (c) The prediction curve based on ωDPSO-LSSVM. Full article ">Figure 10
Modeling data training for the different SSMI methods. (a) The training curve based on LSSVM; (b) The training curve based on PSO-LSSVM; (c) The training curve based on ωDPSO-LSSVM. Full article ">Figure 11
Prediction of test data by the different SSMI methods. (a) The prediction curve based on LSSVM; (b) The prediction curve based on PSO-LSSVM; (c) The prediction curve based on ωDPSO-LSSVM. Full article ">

20 pages, 431 KiB

Open AccessArticle

Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time

by Igor V. Kanatchikov

Symmetry 2019, 11(11), 1413; https://doi.org/10.3390/sym11111413 - 15 Nov 2019

Cited by 5 | Viewed by 2363

Abstract

The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended [...] Read more.

The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended to arbitrary curved space-times. In the limiting case when the inverse of the ultraviolet parameter

ϰ

introduced by precanonical quantization is mapped to the infinitesimal invariant spatial volume element, the canonical functional derivative Schrödinger equation is derived from the manifestly covariant partial derivative precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional spatial product integral of Clifford-algebra-valued precanonical wave function or the product integral of a scalar function obtained from the precanonical wave function by a sequence of transformations. In non-static space-times, the transformations include a nonlocal transformation given by the time-ordered exponential of the zero-th component of spin-connection. Full article

(This article belongs to the Special Issue Space-Time and Symmetry Properties: Classical and Quantum Descriptions)

21 pages, 6094 KiB

Open AccessArticle

Enhanced Membrane Computing Algorithm for SAT Problems Based on the Splitting Rule

by Le Hao and Jun Liu

Symmetry 2019, 11(11), 1412; https://doi.org/10.3390/sym11111412 - 15 Nov 2019

Cited by 3 | Viewed by 2143

Abstract

Boolean propositional satisfiability (SAT) problem is one of the most widely studied NP-complete problems and plays an outstanding role in many domains. Membrane computing is a branch of natural computing which has been proven to solve NP problems in polynomial time with a [...] Read more.

Boolean propositional satisfiability (SAT) problem is one of the most widely studied NP-complete problems and plays an outstanding role in many domains. Membrane computing is a branch of natural computing which has been proven to solve NP problems in polynomial time with a parallel compute mode. This paper proposes a new algorithm for SAT problem which combines the traditional membrane computing algorithm of SAT problem with a classic simplification rule, the splitting rule, which can divide a clause set into two axisymmetric subsets, deal with them respectively and simultaneously, and obtain the solution of the original clause set with the symmetry of their solutions. The new algorithm is shown to be able to reduce the space complexity by distributing clauses with the splitting rule repeatedly, and also reduce both time and space complexity by executing one-literal rule and pure-literal rule as many times as possible. Full article

(This article belongs to the Special Issue Symmetry and Complexity 2019)

► Show Figures

Graphical abstract

16 pages, 507 KiB

Open AccessArticle

Algebraic Properties of the Block Cipher DESL

by Kenneth Matheis, Rainer Steinwandt and Adriana Suárez Corona

Symmetry 2019, 11(11), 1411; https://doi.org/10.3390/sym11111411 - 15 Nov 2019

Cited by 4 | Viewed by 2640

Abstract

The Data Encryption Standard Lightweight extension (DESL) is a lightweight block cipher which is very similar to DES, but unlike DES uses only a single S-box. This work demonstrates that this block cipher satisfies comparable algebraic properties to DES—namely, the round functions of [...] Read more.

The Data Encryption Standard Lightweight extension (DESL) is a lightweight block cipher which is very similar to DES, but unlike DES uses only a single S-box. This work demonstrates that this block cipher satisfies comparable algebraic properties to DES—namely, the round functions of DESL generate the alternating group and both ciphers resist multiple right-hand sides attacks. Full article

(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)

► Show Figures

Figure 1

15 pages, 1117 KiB

Open AccessArticle

Modified Power-Symmetric Distribution

by Emilio Gómez-Déniz, Yuri A. Iriarte, Enrique Calderín-Ojeda and Héctor W. Gómez

Symmetry 2019, 11(11), 1410; https://doi.org/10.3390/sym11111410 - 15 Nov 2019

Cited by 4 | Viewed by 3118

Abstract

In this paper, a general class of modified power-symmetric distributions is introduced. By choosing as symmetric model the normal distribution, the modified power-normal distribution is obtained. For the latter model, some of its more relevant statistical properties are examined. Parameters estimation is carried [...] Read more.

In this paper, a general class of modified power-symmetric distributions is introduced. By choosing as symmetric model the normal distribution, the modified power-normal distribution is obtained. For the latter model, some of its more relevant statistical properties are examined. Parameters estimation is carried out by using the method of moments and maximum likelihood estimation. A simulation analysis is accomplished to study the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the modified power-normal distribution with other existing distributions in the literature by using a real dataset. Full article

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

► Show Figures

Figure 1

22 pages, 5959 KiB

Open AccessArticle

Bat Optimized Link State Routing Protocol for Energy-Aware Mobile Ad-Hoc Networks

by Mohammed Ahmed Jubair, Salama A. Mostafa, Ravie Chandren Muniyandi, Hairulnizam Mahdin, Aida Mustapha, Mustafa Hamid Hassan, Moamin A. Mahmoud, Yasir Amer Al-Jawhar, Ahmed Salih Al-Khaleefa and Ahmed Jubair Mahmood

Symmetry 2019, 11(11), 1409; https://doi.org/10.3390/sym11111409 - 15 Nov 2019

Cited by 51 | Viewed by 5868

Abstract

Mobile ad hoc network (MANET) can be described as a group of wireless mobile nodes that form a temporary dynamic and independent infrastructure network or a central administration facility. High energy consumption is one of the main problems associated with the MANET technology. [...] Read more.

Mobile ad hoc network (MANET) can be described as a group of wireless mobile nodes that form a temporary dynamic and independent infrastructure network or a central administration facility. High energy consumption is one of the main problems associated with the MANET technology. The wireless mobile nodes used in this process rely on batteries because the network does not have a steady power supply. Thus, the rapid battery drain reduces the lifespan of the network. In this paper, a new Bat Optimized Link State Routing (BOLSR) protocol is proposed to improve the energy usage of the Optimized Link State Routing (OLSR) protocol in the MANET. The symmetry between OLSR of MANET and Bat Algorithm (BA) is that both of them use the same mechanism for finding the path via sending and receiving specific signals. This symmetry resulted in the BOLSR protocol that determines the optimized path from a source node to a destination node according to the energy dynamics of the nodes. The BOLSR protocol is implemented in a MANET simulation by using MATLAB toolbox. Different scenarios are tested to compare the BOLSR protocol with the Cellular Automata African Buffalo Optimization (CAABO), Energy-Based OLSR (EBOLSR), and the standard OLSR. The performance metric consists of routing overhead ratios, energy consumption, and end-to-end delay which is applied to evaluate the performance of the routing protocols. The results of the tests reveal that the BOLSR protocol reduces the energy consumption and increases the lifespan of the network, compared with the CAABO, EBOLSR, and OLSR. Full article

► Show Figures

Figure 1

11 pages, 914 KiB

Open AccessArticle

Deep Recurrent Neural Network and Data Filtering for Rumor Detection on Sina Weibo

by Yichun Xu, Chen Wang, Zhiping Dan, Shuifa Sun and Fangmin Dong

Symmetry 2019, 11(11), 1408; https://doi.org/10.3390/sym11111408 - 15 Nov 2019

Cited by 18 | Viewed by 3368

Abstract

Social media makes it easy for individuals to publish and consume news, but it also facilitates the spread of rumors. This paper proposes a novel deep recurrent neural model with a symmetrical network architecture for automatic rumor detection in social media such as [...] Read more.

Social media makes it easy for individuals to publish and consume news, but it also facilitates the spread of rumors. This paper proposes a novel deep recurrent neural model with a symmetrical network architecture for automatic rumor detection in social media such as Sina Weibo, which shows better performance than the existing methods. In the data preparing phase, we filter the posts according to the followers of the user. We then use sequential encoding for the posts and multiple embedding layers to get better feature representation, and multiple recurrent neural network layers to capture the dynamic temporal signals characteristic. The experimental results on the Sina Weibo dataset show that: 1. the sequential encoding performs better than the term frequency-inverse document frequency (TF-IDF) or the doc2vec encoding scheme; 2. the model is more accurate when trained on the posts from the users with more followers; and 3. the model achieves superior improvements over the existing works on the accuracy of detection, including the early detection. Full article

► Show Figures

Figure 1

17 pages, 799 KiB

Open AccessArticle

Normal-G Class of Probability Distributions: Properties and Applications

by Fábio V. J. Silveira, Frank Gomes-Silva, Cícero C. R. Brito, Moacyr Cunha-Filho, Felipe R. S. Gusmão and Sílvio F. A. Xavier-Júnior

Symmetry 2019, 11(11), 1407; https://doi.org/10.3390/sym11111407 - 15 Nov 2019

Cited by 5 | Viewed by 2728

Abstract

In this paper, we propose a novel class of probability distributions called Normal-G. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifiability whenever [...] Read more.

In this paper, we propose a novel class of probability distributions called Normal-G. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifiability whenever the baseline is identifiable. We present special Normal-G sub-models, which can fit asymmetrical data with either positive or negative skew. Other important mathematical properties are described, such as the series expansion of the probability density function (pdf), which is used to derive expressions for the moments and the moment generating function (mgf). We bring Monte Carlo simulation studies to investigate the behavior of the maximum likelihood estimates (MLEs) of two distributions generated by the class and we also present applications to real datasets to illustrate its usefulness. Full article

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

► Show Figures

Figure 1

16 pages, 350 KiB

Open AccessArticle

Ideals of Numerical Semigroups and Error-Correcting Codes

by Maria Bras-Amorós

Symmetry 2019, 11(11), 1406; https://doi.org/10.3390/sym11111406 - 14 Nov 2019

Cited by 2 | Viewed by 2559

Abstract

Several results relating additive ideals of numerical semigroups and algebraic-geometry
codes are presented. In particular, we deal with the set of non-redundant parity-checks, the code
length, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometry
codes from the perspective of the related [...] Read more.

Several results relating additive ideals of numerical semigroups and algebraic-geometry
codes are presented. In particular, we deal with the set of non-redundant parity-checks, the code
length, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometry
codes from the perspective of the related Weierstrass semigroups. These results are related to
cryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, network
coding, and ramp secret sharing schemes. Full article

(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)

17 pages, 5231 KiB

Open AccessFeature PaperArticle

Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation

by Eunchan Jo, Byungmoon Kim and Oh-Young Song

Symmetry 2019, 11(11), 1405; https://doi.org/10.3390/sym11111405 - 14 Nov 2019

Cited by 1 | Viewed by 3251

Abstract

We propose a new hybrid simulation method to model burning solid interactions. Unlike gas fuel, fire and smoke interactions that have been relatively well studied in the past, simulations of solid fuel combustion processes remain largely unaddressed. These include pyrolysis/smoldering, interactions with oxygen [...] Read more.

We propose a new hybrid simulation method to model burning solid interactions. Unlike gas fuel, fire and smoke interactions that have been relatively well studied in the past, simulations of solid fuel combustion processes remain largely unaddressed. These include pyrolysis/smoldering, interactions with oxygen and flow inside porous solid. To advance this simulation problem, we designed a new hybrid of the Lattice-Boltzmann method (LBM) and a Eulerian grid based Navier-Stokes equation (NSE). It uses the LBM, which has symmetrical directions of particle velocities in a cell, for inside the solid fuel and the NSE, which has a representative velocity in a cell, for outside the solid. At the interface where the two methods join, we develop a novel method to exchange physical quantities and show a natural transition between the two methods. Since LBM allows us to directly manage the quantity of exchanges from the microscopic perspective, that is, between lattice points, we can easily simulate the burning speed and the shape change of burning an inhomogeneous solid. Also, we derive an LBM version of the previously proposed porous Navier-Stokes equation to simulate gas flow inside the porous solid. In addition, we use the NS solver outside the solid where macroscopic behavior is much more dominant and, hence, LBM is less efficient than NS solver. Our results show us the physical stability and accuracy and visual realism. Full article

► Show Figures

Figure 1

12 pages, 426 KiB

Open AccessArticle

Volume Preserving Maps Between p-Balls

by Adrian Holhoş and Daniela Roşca

Symmetry 2019, 11(11), 1404; https://doi.org/10.3390/sym11111404 - 14 Nov 2019

Viewed by 1960

Abstract

We construct a volume preserving map

U_{p}

from the p-ball

B_{p} (r) = \{x \in R^{3}, {∥ x ∥}_{p} \leq r\}

to the regular octahedron

B_{1} (r^{'})

, for arbitrary [...] Read more.

We construct a volume preserving map

U_{p}

from the p-ball

B_{p} (r) = \{x \in R^{3}, {∥ x ∥}_{p} \leq r\}

to the regular octahedron

B_{1} (r^{'})

, for arbitrary

p > 0

. Then we calculate the inverse

U_{p}^{- 1}

and we also deduce explicit expressions for

U_{\infty}

and

U_{\infty}^{- 1} .

This allows us to construct volume preserving maps between arbitrary balls

B_{p} (r)

and

B_{p^{'}} (\tilde{r})

, and also to map uniform and refinable grids between them. Finally we list some possible applications of our maps. Full article

(This article belongs to the Special Issue Symmetry in Applied Mathematics)

► Show Figures

Figure 1

18 pages, 4161 KiB

Open AccessArticle

Quasi-Periodic Oscillating Flows in a Channel with a Suddenly Expanded Section

by Takuya Masuda and Toshio Tagawa

Symmetry 2019, 11(11), 1403; https://doi.org/10.3390/sym11111403 - 13 Nov 2019

Cited by 4 | Viewed by 3899

Abstract

In this study, two-dimensional numerical simulation was carried out for an oscillatory flow between parallel flat plates having a suddenly expanded section. Governing equations were discretized with the second-order accuracy by a finite volume method on an unequal interval mesh system resolving finer [...] Read more.

In this study, two-dimensional numerical simulation was carried out for an oscillatory flow between parallel flat plates having a suddenly expanded section. Governing equations were discretized with the second-order accuracy by a finite volume method on an unequal interval mesh system resolving finer near walls and corners to obtain the characteristics of the oscillatory flow accurately. Amplitude spectrums of a velocity component were obtained to investigate the periodic characteristics of the oscillatory flow. At low Reynolds numbers, the flow is periodic because the spectrum mostly consists of harmonic components, and then at high Reynolds numbers, it transits to a quasi-periodic flow mixed with non-harmonic components. In conjunction with the periodic oscillation of a main flow, separation vortices that are not uniform in size are generated from the corner of a sudden contraction part and pass through a downstream region coming into contact with the wall. The number of the vortices decreases rapidly after they are generated, but the vortices are generated again in the downstream region. In order to specify where aperiodicity is generated, the turbulent kinetic energy is introduced, and it is decomposed into the harmonic and non-harmonic components. The peaks of the non-harmonic component are generated in the region of the expanded section. Full article

(This article belongs to the Special Issue Symmetry in Fluid Flow)

► Show Figures

Graphical abstract

14 pages, 262 KiB

Open AccessArticle

Some Inequalities Using Generalized Convex Functions in Quantum Analysis

by Miguel J. Vivas-Cortez, Artion Kashuri, Rozana Liko and Jorge E. Hernández Hernández

Symmetry 2019, 11(11), 1402; https://doi.org/10.3390/sym11111402 - 13 Nov 2019

Cited by 22 | Viewed by 2417

Abstract

In the present work, the Hermite–Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in

(0, 1]

and two arbitrary real functions defined on [...] Read more.

In the present work, the Hermite–Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in

(0, 1]

and two arbitrary real functions defined on

[0, 1]

. From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions and the methodology used reveals, in a sense, a symmetric mathematical phenomenon. In addition, the definition of dominated convex functions with respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established. Full article

13 pages, 261 KiB

Open AccessArticle

Spacetime and Deformations of Special Relativistic Kinematics

by José Manuel Carmona, José Luis Cortés and José Javier Relancio

Symmetry 2019, 11(11), 1401; https://doi.org/10.3390/sym11111401 - 12 Nov 2019

Cited by 14 | Viewed by 2446

Abstract

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction [...] Read more.

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction processes, for which absolute locality in terms of canonical spacetime coordinates is lost. We discuss the different alternatives for observable effects in the propagation of a particle over very large distances that emerge from the new notion of spacetime. A central ingredient in the discussion is the cluster decomposition principle, which can be used to favor some alternatives over the others. Full article

(This article belongs to the Special Issue Symmetry and Quantum Gravity)

22 pages, 2516 KiB

Open AccessArticle

Novel Fuzzy Clustering Methods for Test Case Prioritization in Software Projects

by A. D. Shrivathsan, K. S. Ravichandran, R. Krishankumar, V. Sangeetha, Samarjit Kar, Pawel Ziemba and Jaroslaw Jankowski

Symmetry 2019, 11(11), 1400; https://doi.org/10.3390/sym11111400 - 12 Nov 2019

Cited by 10 | Viewed by 3704

Abstract

Systematic Regression Testing is essential for maintaining software quality, but the cost of regression testing is high. Test case prioritization (TCP) is a widely used approach to reduce this cost. Many researchers have proposed regression test case prioritization techniques, and clustering is one [...] Read more.

Systematic Regression Testing is essential for maintaining software quality, but the cost of regression testing is high. Test case prioritization (TCP) is a widely used approach to reduce this cost. Many researchers have proposed regression test case prioritization techniques, and clustering is one of the popular methods for prioritization. The task of selecting appropriate test cases and identifying faulty functions involves ambiguities and uncertainties. To alleviate the issue, in this paper, two fuzzy-based clustering techniques are proposed for TCP using newly derived similarity coefficient and dominancy measure. Proposed techniques adopt grouping technology for clustering and the Weighted Arithmetic Sum Product Assessment (WASPAS) method for ranking. Initially, test cases are clustered using similarity//dominancy measures, which are later prioritized using the WASPAS method under both inter- and intra-perspectives. The proposed algorithms are evaluated using real-time data obtained from Software-artifact Infrastructure Repository (SIR). On evaluation, it is inferred that the proposed algorithms increase the likelihood of selecting more relevant test cases when compared to the recent state-of-the-art techniques. Finally, the strengths of the proposed algorithms are discussed in comparison with state-of-the-art techniques. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

► Show Figures

Figure 1

23 pages, 7663 KiB

Open AccessArticle

A Haptic Model of Entanglement, Gauge Symmetries and Minimal Interaction Based on Knot Theory

by Stefan Heusler and Malte Ubben

Symmetry 2019, 11(11), 1399; https://doi.org/10.3390/sym11111399 - 12 Nov 2019

Cited by 4 | Viewed by 3952

Abstract

The Heegaard splitting of

S U (2)

is a particularly useful representation for quantum phases of spin j-representation arising in the mapping

S_{1} \to S_{3}

, which can be related to

(2 j, 2)

torus [...] Read more.

The Heegaard splitting of

S U (2)

is a particularly useful representation for quantum phases of spin j-representation arising in the mapping

S_{1} \to S_{3}

, which can be related to

(2 j, 2)

torus knots in Hilbert space. We show that transitions to homotopically equivalent knots can be associated with gauge invariance, and that the same mechanism is at the heart of quantum entanglement. In other words, (minimal) interaction causes entanglement. Particle creation is related to cuts in the knot structure. We show that inner twists can be associated with operations with the quaternions

(I, J, K)

, which are crucial to understand the Hopf mapping

S_{3} \to S_{2}

. We discuss the relationship between observables on the Bloch sphere

S_{2}

, and knots with inner twists in Hilbert space. As applications, we discuss selection rules in atomic physics, and the status of virtual particles arising in Feynman diagrams. Using a simple paper strip model revealing the knot structure of quantum phases in Hilbert space including inner twists, a

h a p t i c

model of entanglement and gauge symmetries is proposed, which may also be valid for physics education. Full article

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry, Volume 11, Issue 11 (November 2019) – 103 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI