Symmetry

11 pages, 4143 KiB

Open AccessEditor’s ChoiceArticle

The Immobilization of Oxindole Derivatives with Use of Cube Rhombellane Homeomorphs

by Przemysław Czeleń and Beata Szefler

Symmetry 2019, 11(7), 900; https://doi.org/10.3390/sym11070900 - 10 Jul 2019

Cited by 8 | Viewed by 2517

A key aspect of modern drug research is the development of delivery methods that ensure the possibility of implementing targeted therapy for a specific biological target. The use of nanocarriers enables to achieve this objective, also allowing to reduce the toxicity of used [...] Read more.

A key aspect of modern drug research is the development of delivery methods that ensure the possibility of implementing targeted therapy for a specific biological target. The use of nanocarriers enables to achieve this objective, also allowing to reduce the toxicity of used substances and often extending their bioavailability. Through the application of docking methods, the possibility of using cube rhombellanes as potential carriers for two oxindole derivatives was analyzed. In the studies, compounds identified as inhibitors of the CDK2 enzyme and a set of nanostructures proposed by the Topo Cluj Group were used. The popular fullerene molecule C₆₀ was used as the reference system. The estimated binding affinities and structures of obtained complexes show that use of functionalized cube rhombellanes containing hydrogen bond donors and acceptors in their external molecular shell significantly increases ligand affinity toward considered nanocariers, compared to classic fullerenes. The presented values also allow to state that an important factor determining the mutual affinity of the tested ligands and nanostructures is the symmetry of the analyzed nanocarriers and its influence on the distribution of binding groups (aromatic systems, donors and acceptors of hydrogen bonds) on the surface of nanoparticles. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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11 pages, 3127 KiB

Open AccessEditor’s ChoiceArticle

Docking of Cisplatin on Fullerene Derivatives and Some Cube Rhombellane Functionalized Homeomorphs

by Beata Szefler and Przemysław Czeleń

Symmetry 2019, 11(7), 874; https://doi.org/10.3390/sym11070874 (registering DOI) - 3 Jul 2019

Cited by 9 | Viewed by 3070

Abstract

Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed [...] Read more.

Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins of the B group, containing aromatic rings with lone-pair orbitals. This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus. That is why it seems to be important to connect CisPt with nanostructures and in this way prevent the drug from combining with the B vitamins. As a proposal for a new nanodrug, an attempt was made to implement Cispaltin (CisPt) ligand on functionalized C₆₀ fullerenes and on a cube rhombellane homeomorphic surface. The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers. The behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C₆₀, in terms of their (interacting) energy, geometry and topology was studied and a detailed analysis of structural properties after docking showed many interesting features. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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16 pages, 326 KiB

Open AccessEditor’s ChoiceArticle

On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

by M. Marin, S. Vlase, R. Ellahi and M.M. Bhatti

Symmetry 2019, 11(7), 863; https://doi.org/10.3390/sym11070863 - 2 Jul 2019

Cited by 115 | Viewed by 3611

Abstract

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based [...] Read more.

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem. Full article

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

15 pages, 2365 KiB

Open AccessEditor’s ChoiceArticle

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

by Lorentz Jäntschi

Symmetry 2019, 11(6), 835; https://doi.org/10.3390/sym11060835 - 25 Jun 2019

Cited by 38 | Viewed by 6997

Abstract

One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling [...] Read more.

One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution. Full article

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

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16 pages, 1724 KiB

Open AccessEditor’s ChoiceConcept Paper

Chemical Basis of Biological Homochirality during the Abiotic Evolution Stages on Earth

by Josep M. Ribó and David Hochberg

Symmetry 2019, 11(6), 814; https://doi.org/10.3390/sym11060814 - 20 Jun 2019

Cited by 19 | Viewed by 3863

Abstract

Spontaneous mirror symmetry breaking (SMSB), a phenomenon leading to non-equilibrium stationary states (NESS) that exhibits biases away from the racemic composition is discussed here in the framework of dissipative reaction networks. Such networks may lead to a metastable racemic non-equilibrium stationary state that [...] Read more.

Spontaneous mirror symmetry breaking (SMSB), a phenomenon leading to non-equilibrium stationary states (NESS) that exhibits biases away from the racemic composition is discussed here in the framework of dissipative reaction networks. Such networks may lead to a metastable racemic non-equilibrium stationary state that transforms into one of two degenerate but stable enantiomeric NESSs. In such a bifurcation scenario, the type of the reaction network, as well the boundary conditions, are similar to those characterizing the currently accepted stages of emergence of replicators and autocatalytic systems. Simple asymmetric inductions by physical chiral forces during previous stages of chemical evolution, for example in astrophysical scenarios, must involve unavoidable racemization processes during the time scales associated with the different stages of chemical evolution. However, residual enantiomeric excesses of such asymmetric inductions suffice to drive the SMSB stochastic distribution of chiral signs into a deterministic distribution. According to these features, we propose that a basic model of the chiral machinery of proto-life would emerge during the formation of proto-cell systems by the convergence of the former enantioselective scenarios. Full article

(This article belongs to the Special Issue Possible Scenarios for Homochirality on Earth)

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13 pages, 1568 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept

by Paweł Więcek, Daniel Kubek, Jan Hipolit Aleksandrowicz and Aleksandra Stróżek

Symmetry 2019, 11(6), 755; https://doi.org/10.3390/sym11060755 - 4 Jun 2019

Cited by 13 | Viewed by 3683

Abstract

Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, [...] Read more.

Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, in addition to criteria such as punctuality, the frequency of departures, and the number of transfers, a travelling comfort level is an important element for passengers. An overcrowded bus may discourage travelers from choosing this mode of transport and induce them to use a private car despite the existence of many other facilities offered by a given public transport system. Therefore, the forecasting of bus passenger demand, as well as bus occupancy at individual bus stops, is currently an important research direction. The main goal of the article is to present the conceptual framework for the Advanced Travel Information System with the prediction module. The proposed approach assumes that the prediction module is based on the use of the Markov Chain concept. The efficiency and accuracy of the obtained prediction were presented based on a real-life example, where the measurements of passengers boarding and alighting at bus stops were made in a selected Cracow bus line. The methodology presented in the paper and the obtained results can significantly contribute to the development of solutions and systems for a better management as well as a cost and energy consumption optimisation in the public transport system. Current and forecasted information related to bus occupancy, when properly used in the travel information system, may have a positive impact on the development of urban mobility patterns by encouraging the use of public transport. This article addresses the current and practical research problem using an adequate theoretical mathematical tool to describe it, reflecting the characteristics and nature of the phenomenon being studied. To the best of the authors’ knowledge, the article deals for the first time with the problem of prediction of onboard bus comfort levels based on in-vehicle occupancy. Full article

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

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20 pages, 3398 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Role of Asymmetric Autocatalysis in the Elucidation of Origins of Homochirality of Organic Compounds

by Kenso Soai, Tsuneomi Kawasaki and Arimasa Matsumoto

Symmetry 2019, 11(5), 694; https://doi.org/10.3390/sym11050694 - 20 May 2019

Cited by 24 | Viewed by 4913

Abstract

Pyrimidyl alkanol and related compounds were found to be asymmetric autocatalysts in the enantioselective addition of diisopropylzinc to pyrimidine-5-carbaldehyde and related aldehydes. In the asymmetric autocatalysis with amplification of enantiomeric excess (ee), the very low ee (ca. 0.00005%) of 2-alkynyl-5-pyrimidyl alkanol was significantly [...] Read more.

Pyrimidyl alkanol and related compounds were found to be asymmetric autocatalysts in the enantioselective addition of diisopropylzinc to pyrimidine-5-carbaldehyde and related aldehydes. In the asymmetric autocatalysis with amplification of enantiomeric excess (ee), the very low ee (ca. 0.00005%) of 2-alkynyl-5-pyrimidyl alkanol was significantly amplified to >99.5% ee with an increase in the amount. By using asymmetric autocatalysis with amplification of ee, several origins of homochirality have been examined. Circularly polarized light, chiral quartz, and chiral crystals formed from achiral organic compounds such as glycine and carbon (¹³C/¹²C), nitrogen (¹⁵N/¹⁴N), oxygen (¹⁸O/¹⁶O), and hydrogen (D/H) chiral isotopomers were found to act as the origin of chirality in asymmetric autocatalysis. And the spontaneous absolute asymmetric synthesis was also realized without the intervention of any chiral factor. Full article

(This article belongs to the Special Issue Possible Scenarios for Homochirality on Earth)

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20 pages, 256 KiB

Open AccessEditor’s ChoiceArticle

Conservation Laws and Stability of Field Theories of Derived Type

by Dmitry S. Kaparulin

Symmetry 2019, 11(5), 642; https://doi.org/10.3390/sym11050642 - 7 May 2019

Cited by 12 | Viewed by 2094

Abstract

We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time [...] Read more.

We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by n-th-order polynomial then this series includes n independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an n-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern–Simons theory. Full article

(This article belongs to the Special Issue Noether's Theorem and Symmetry)

14 pages, 281 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials

by Dae San Kim, Han Young Kim, Dojin Kim and Taekyun Kim

Symmetry 2019, 11(5), 613; https://doi.org/10.3390/sym11050613 - 2 May 2019

Cited by 16 | Viewed by 2248

Abstract

The main purpose of this paper is to give several identities of symmetry for type 2 Bernoulli and Euler polynomials by considering certain quotients of bosonic p-adic and fermionic p-adic integrals on

Z_{p}

, where p is an odd prime [...] Read more.

The main purpose of this paper is to give several identities of symmetry for type 2 Bernoulli and Euler polynomials by considering certain quotients of bosonic p-adic and fermionic p-adic integrals on

Z_{p}

, where p is an odd prime number. Indeed, they are symmetric identities involving type 2 Bernoulli polynomials and power sums of consecutive odd positive integers, and the ones involving type 2 Euler polynomials and alternating power sums of odd positive integers. Furthermore, we consider two random variables created from random variables having Laplace distributions and show their moments are given in terms of the type 2 Bernoulli and Euler numbers. Full article

(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ)

16 pages, 4383 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Hay Inclined Plane in Coalbrookdale (Shropshire, England): Geometric Modeling and Virtual Reconstruction

by José Ignacio Rojas-Sola and Eduardo De la Morena-De la Fuente

Symmetry 2019, 11(4), 589; https://doi.org/10.3390/sym11040589 - 24 Apr 2019

Cited by 17 | Viewed by 3526

Abstract

This article shows the geometric modeling and virtual reconstruction of the inclined plane of Coalbrookdale (Shropshire, England) that was in operation from 1792 to 1894. This historical invention, work of the Englishman William Reynolds, allowed the transportation of boats through channels located at [...] Read more.

This article shows the geometric modeling and virtual reconstruction of the inclined plane of Coalbrookdale (Shropshire, England) that was in operation from 1792 to 1894. This historical invention, work of the Englishman William Reynolds, allowed the transportation of boats through channels located at different levels. Autodesk Inventor Professional software has been used to obtain the 3D CAD model of this historical invention and its geometric documentation. The material for the research is available on the website of the Betancourt Project of the Canary Orotava Foundation for the History of Science. Also, because the single sheet does not have a scale, it has been necessary to adopt a graphic scale so that the dimensions of the different elements are coherent. Furthermore, it has been necessary to establish some dimensional, geometric, and movement restrictions (degrees of freedom) so that the set will work properly. One of the main conclusions is that William Reynolds designed a mechanism seeking a longitudinal symmetry so that, from a single continuous movement, the mechanism allows two vessels to ascend and descend simultaneously. This engineering solution facilitated a doubling of the working capacity of the device, as well as a reduction of the energy needs of the system. Full article

(This article belongs to the Special Issue Symmetry in Engineering Sciences)

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46 pages, 594 KiB

Open AccessEditor’s ChoiceArticle

Hadronic and Hadron-Like Physics of Dark Matter

by Vitaly Beylin, Maxim Yu. Khlopov, Vladimir Kuksa and Nikolay Volchanskiy

Symmetry 2019, 11(4), 587; https://doi.org/10.3390/sym11040587 - 23 Apr 2019

Cited by 28 | Viewed by 3660

Abstract

The problems of simple elementary weakly interacting massive particles (WIMPs) appeal to extend the physical basis for nonbaryonic dark matter. Such extension involves more sophisticated dark matter candidates from physics beyond the Standard Model (BSM) of elementary particles. We discuss several models of [...] Read more.

The problems of simple elementary weakly interacting massive particles (WIMPs) appeal to extend the physical basis for nonbaryonic dark matter. Such extension involves more sophisticated dark matter candidates from physics beyond the Standard Model (BSM) of elementary particles. We discuss several models of dark matter, predicting new colored, hyper-colored or techni-colored particles and their accelerator and non-accelerator probes. The nontrivial properties of the proposed dark matter candidates can shed new light on the dark matter physics. They provide interesting solutions for the puzzles of direct and indirect dark matter search. Full article

(This article belongs to the Special Issue Cosmological Inflation, Dark Matter and Dark Energy)

8 pages, 4083 KiB

Open AccessEditor’s ChoiceArticle

Fully Metallic Flat Lens Based on Locally Twist-Symmetric Array of Complementary Split-Ring Resonators

by Oskar Dahlberg, Guido Valerio and Oscar Quevedo-Teruel

Symmetry 2019, 11(4), 581; https://doi.org/10.3390/sym11040581 - 22 Apr 2019

Cited by 16 | Viewed by 3994

Abstract

In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of [...] Read more.

In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of complementary split-ring resonators. In this specific design, the twist symmetry is local, as it is only applied to the unit cell of the array. Moreover, the twist symmetry is an approximation, as it is only applied to part of the unit cell. First, we demonstrate that, by varying the order of twist symmetry, the phase delay experienced by a wave propagating through the array can be accurately controlled. Secondly, a lens is designed by tailoring the unit cells throughout the aperture of the lens in order to obtain the desired phase delay. Simulation and measurement results demonstrate that the lens successfully transforms a spherical wave emanating from the focal point into a plane wave at the opposite side of the lens. The demonstrated concepts find application in future wireless communication networks where fully-metallic directive antennas are desired. Full article

(This article belongs to the Special Issue Higher Symmetries and Its Application in Microwave Technology, Antennas and Metamaterials)

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14 pages, 659 KiB

Open AccessEditor’s ChoiceArticle

A Scalable and Hybrid Intrusion Detection System Based on the Convolutional-LSTM Network

by Muhammad Ashfaq Khan, Md. Rezaul Karim and Yangwoo Kim

Symmetry 2019, 11(4), 583; https://doi.org/10.3390/sym11040583 - 22 Apr 2019

Cited by 115 | Viewed by 12548

Abstract

With the rapid advancements of ubiquitous information and communication technologies, a large number of trustworthy online systems and services have been deployed. However, cybersecurity threats are still mounting. An intrusion detection (ID) system can play a significant role in detecting such security threats. [...] Read more.

With the rapid advancements of ubiquitous information and communication technologies, a large number of trustworthy online systems and services have been deployed. However, cybersecurity threats are still mounting. An intrusion detection (ID) system can play a significant role in detecting such security threats. Thus, developing an intelligent and accurate ID system is a non-trivial research problem. Existing ID systems that are typically used in traditional network intrusion detection system often fail and cannot detect many known and new security threats, largely because those approaches are based on classical machine learning methods that provide less focus on accurate feature selection and classification. Consequently, many known signatures from the attack traffic remain unidentifiable and become latent. Furthermore, since a massive network infrastructure can produce large-scale data, these approaches often fail to handle them flexibly, hence are not scalable. To address these issues and improve the accuracy and scalability, we propose a scalable and hybrid IDS, which is based on Spark ML and the convolutional-LSTM (Conv-LSTM) network. This IDS is a two-stage ID system: the first stage employs the anomaly detection module, which is based on Spark ML. The second stage acts as a misuse detection module, which is based on the Conv-LSTM network, such that both global and local latent threat signatures can be addressed. Evaluations of several baseline models in the ISCX-UNB dataset show that our hybrid IDS can identify network misuses accurately in 97.29% of cases and outperforms state-of-the-art approaches during 10-fold cross-validation tests. Full article

(This article belongs to the Special Issue Symmetry-Adapted Machine Learning for Information Security)

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Graphical abstract

22 pages, 349 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Imaginary Chemical Potential, NJL-Type Model and Confinement–Deconfinement Transition

by Kouji Kashiwa

Symmetry 2019, 11(4), 562; https://doi.org/10.3390/sym11040562 - 18 Apr 2019

Cited by 13 | Viewed by 2968

Abstract

In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss [...] Read more.

In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss periodicity and the transition. We summarize how these properties play a crucial role in understanding QCD properties at finite temperature and density. This review covers several topics in the investigation of the QCD phase diagram based on the imaginary chemical potential. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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10 pages, 238 KiB

Open AccessEditor’s ChoiceArticle

Hyers-Ulam Stability for Linear Differences with Time Dependent and Periodic Coefficients

by Constantin Buşe, Donal O’Regan and Olivia Saierli

Symmetry 2019, 11(4), 512; https://doi.org/10.3390/sym11040512 - 9 Apr 2019

Cited by 12 | Viewed by 2004

Abstract

Let

q \geq 2

be a positive integer and let

(a_{j})

,

(b_{j})

, and

(c_{j})

(with j a non-negative integer) be three given

C

-valued and q-periodic sequences. Let [...] Read more.

Let

q \geq 2

be a positive integer and let

(a_{j})

,

(b_{j})

, and

(c_{j})

(with j a non-negative integer) be three given

C

-valued and q-periodic sequences. Let

A (q) : = A_{q - 1} \dots A_{0}

, where

A_{j}

is as is given below. Assuming that the “monodromy matrix”

A (q)

has at least one multiple eigenvalue, we prove that the linear scalar recurrence

x_{n + 3} = a_{n} x_{n + 2} + b_{n} x_{n + 1} + c_{n} x_{n}, n \in Z_{+}

is Hyers-Ulam stable if and only if the spectrum of

A (q)

does not intersect the unit circle

Γ : = {w \in C : | w | = 1}

. Connecting this result with a recently obtained one it follows that the above linear recurrence is Hyers-Ulam stable if and only if the spectrum of

A (q)

does not intersect the unit circle. Full article

(This article belongs to the Special Issue Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry)

18 pages, 409 KiB

Open AccessEditor’s ChoiceReview

Cosmological Probes of Supersymmetric Field Theory Models at Superhigh Energy Scales

by Sergei V. Ketov and Maxim Yu. Khlopov

Symmetry 2019, 11(4), 511; https://doi.org/10.3390/sym11040511 - 9 Apr 2019

Cited by 39 | Viewed by 3392

Abstract

The lack of positive results in searches for supersymmetric (SUSY) particles at the Large Hadron Collider (LHC) and in direct searches for Weakly Interacting Massive Particles (WIMPs) in the underground experiments may hint to a super-high energy scale of SUSY phenomena beyond the [...] Read more.

The lack of positive results in searches for supersymmetric (SUSY) particles at the Large Hadron Collider (LHC) and in direct searches for Weakly Interacting Massive Particles (WIMPs) in the underground experiments may hint to a super-high energy scale of SUSY phenomena beyond the reach of direct experimental probes. At such scales the supergravity models based on Starobinsky inflation can provide the mechanisms for both inflation and superheavy dark matter. However, it makes the indirect methods the only way of testing the SUSY models, so that cosmological probes acquire the special role in this context. Such probes can rely on the nontrivial effects of SUSY physics in the early Universe, which are all model-dependent and thus can provide discrimination of the models and their parameters. The nonstandard cosmological features like Primordial Black Holes (PBHs) or antimatter domains in a baryon-asymmetric universe are discussed as possible probes for high energy scale SUSY physics. Full article

(This article belongs to the Special Issue Supersymmetric Field Theory 2018)

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31 pages, 1579 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2 + 1) Polyakov-Nambu-Jona-Lasinio Model

by Pedro Costa and Renan Pereira

Symmetry 2019, 11(4), 507; https://doi.org/10.3390/sym11040507 - 8 Apr 2019

Cited by 11 | Viewed by 2963

Abstract

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the (

T, μ_{B})

-plane, with its isentropic trajectories, paying [...] Read more.

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the (

T, μ_{B})

-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change abruptly near the CEP, which can be relevant for its experimental search. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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8 pages, 796 KiB

Open AccessEditor’s ChoiceArticle

Time-reversal Symmetry in Antenna Theory

by Mário G. Silveirinha

Symmetry 2019, 11(4), 486; https://doi.org/10.3390/sym11040486 - 4 Apr 2019

Cited by 10 | Viewed by 3313

Abstract

Here, I discuss some implications of the time-reversal invariance of lossless radiating systems. I highlight that time-reversal symmetry provides a rather intuitive explanation for the conditions of polarization and impedance matching of a receiving antenna. Furthermore, I describe a solution to generate the [...] Read more.

Here, I discuss some implications of the time-reversal invariance of lossless radiating systems. I highlight that time-reversal symmetry provides a rather intuitive explanation for the conditions of polarization and impedance matching of a receiving antenna. Furthermore, I describe a solution to generate the time-reversed electromagnetic field through the illumination of a matched receiving antenna with a Herglotz wave. Full article

(This article belongs to the Special Issue Higher Symmetries and Its Application in Microwave Technology, Antennas and Metamaterials)

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18 pages, 9264 KiB

Open AccessEditor’s ChoiceArticle

One-Plane Glide-Symmetric Holey Structures for Stop-Band and Refraction Index Reconfiguration

by Adrian Tamayo-Dominguez, Jose-Manuel Fernandez-Gonzalez and Oscar Quevedo-Teruel

Symmetry 2019, 11(4), 495; https://doi.org/10.3390/sym11040495 - 4 Apr 2019

Cited by 14 | Viewed by 3565

Abstract

This work presents a new configuration to create glide-symmetric structures in a single plane, which facilitates fabrication and avoids alignment problems in the assembly process compared to traditional glide-symmetric structures based on several planes. The proposed structures can be printed on the metal [...] Read more.

This work presents a new configuration to create glide-symmetric structures in a single plane, which facilitates fabrication and avoids alignment problems in the assembly process compared to traditional glide-symmetric structures based on several planes. The proposed structures can be printed on the metal face of a dielectric substrate, which acts as a support. The article includes a parametric study based on dispersion diagrams on the appearance of stop-bands and phase-shifting by breaking the symmetry. In addition, a procedure to regenerate symmetry is proposed that may be useful for reconfigurable devices. Finally, the measured and simulated S parameters of 10 × 10 unit-cell structures are presented to illustrate the attenuation in these stop-bands and the refractive index of the propagation modes. The attenuation obtained is greater than 30 dB in the stop-band for the symmetry-broken prototype. Full article

(This article belongs to the Special Issue Higher Symmetries and Its Application in Microwave Technology, Antennas and Metamaterials)

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17 pages, 646 KiB

Open AccessEditor’s ChoiceArticle

Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum

by Galina L. Klimchitskaya, Vladimir M. Mostepanenko, René I. P. Sedmik and Hartmut Abele

Symmetry 2019, 11(3), 407; https://doi.org/10.3390/sym11030407 - 20 Mar 2019

Cited by 24 | Viewed by 2432

Abstract

We consider the Cannex (Casimir And Non-Newtonian force EXperiment) test of the quantum vacuum intended for measuring the gradient of the Casimir pressure between two flat parallel plates at large separations and constraining parameters of the chameleon model of dark energy in cosmology. [...] Read more.

We consider the Cannex (Casimir And Non-Newtonian force EXperiment) test of the quantum vacuum intended for measuring the gradient of the Casimir pressure between two flat parallel plates at large separations and constraining parameters of the chameleon model of dark energy in cosmology. A modification of the measurement scheme is proposed that allows simultaneous measurements of both the Casimir pressure and its gradient in one experiment. It is shown that with several improvements the Cannex test will be capable to strengthen the constraints on the parameters of the Yukawa-type interaction by up to an order of magnitude over a wide interaction range. The constraints on the coupling constants between nucleons and axion-like particles, which are considered as the most probable constituents of dark matter, could also be strengthened over a region of axion masses from 1 to 100 meV. Full article

(This article belongs to the Special Issue Cosmology and Quantum Vacuum)

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18 pages, 3272 KiB

Open AccessEditor’s ChoiceArticle

Modelling Construction Site Cost Index Based on Neural Network Ensembles

by Michał Juszczyk and Agnieszka Leśniak

Symmetry 2019, 11(3), 411; https://doi.org/10.3390/sym11030411 - 20 Mar 2019

Cited by 29 | Viewed by 3747

Abstract

Construction site overhead costs are key components of cost estimation in construction projects. The estimates are expected to be accurate, but there is a growing demand to shorten the time necessary to deliver cost estimates. The balancing (symmetry) between time of calculation and [...] Read more.

Construction site overhead costs are key components of cost estimation in construction projects. The estimates are expected to be accurate, but there is a growing demand to shorten the time necessary to deliver cost estimates. The balancing (symmetry) between time of calculation and satisfaction of reliable estimation was the reason for developing a new model for cost estimation in construction. This paper reports some results from the authors’ broad research on the modelling processes in engineering related to estimation of construction costs using artificial intelligence tools. The aim of this work was to develop a model capable of predicting a construction site cost index that would benefit from combining several artificial neural networks into an ensemble. Combining selected neural networks and forming the ensemble-based models compromised their strengths and weaknesses. With the use of data including training patterns collected on the basis of studies of completed construction projects, the authors investigated various types of neural networks in order to select the members of the ensemble. Finally, three models that were assessed in terms of performance and prediction quality were proposed. The results revealed that the developed models based on ensemble averaging and stacked generalisation met the expectations of knowledge generalisation and accuracy of prediction of site overhead cost index. The proposed models offer predictions of cost in an accepted error range and prove to deliver better predictions than those based on single neural networks. The developed tools can be used in the decision-making process regarding construction cost estimation. Full article

(This article belongs to the Special Issue Multi-Criteria Decision-Making Techniques for Improvement Sustainability Engineering Processes)

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28 pages, 373 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

On the Structure of Finite Groupoids and Their Representations

by Alberto Ibort and Miguel A. Rodríguez

Symmetry 2019, 11(3), 414; https://doi.org/10.3390/sym11030414 - 20 Mar 2019

Cited by 9 | Viewed by 3164

Abstract

In this paper, both the structure and the theory of representations of finite groupoids are discussed. A finite connected groupoid turns out to be an extension of the groupoids of pairs of its set of units by its canonical totally disconnected isotropy subgroupoid. [...] Read more.

In this paper, both the structure and the theory of representations of finite groupoids are discussed. A finite connected groupoid turns out to be an extension of the groupoids of pairs of its set of units by its canonical totally disconnected isotropy subgroupoid. An extension of Maschke’s theorem for groups is proved showing that the algebra of a finite groupoid is semisimple and all finite-dimensional linear representations of finite groupoids are completely reducible. The theory of characters for finite-dimensional representations of finite groupoids is developed and it is shown that irreducible representations of the groupoid are in one-to-one correspondence with irreducible representation of its isotropy groups, with an extension of Burnside’s theorem describing the decomposition of the regular representation of a finite groupoid. Some simple examples illustrating these results are exhibited with emphasis on the groupoids interpretation of Schwinger’s description of quantum mechanical systems. Full article

(This article belongs to the Special Issue New trends on Symmetry and Topology in Quantum Mechanics)

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14 pages, 3687 KiB

Open AccessEditor’s ChoiceArticle

Twist and Glide Symmetries for Helix Antenna Design and Miniaturization

by Ángel Palomares-Caballero, Pablo Padilla, Antonio Alex-Amor, Juan Valenzuela-Valdés and Oscar Quevedo-Teruel

Symmetry 2019, 11(3), 349; https://doi.org/10.3390/sym11030349 - 8 Mar 2019

Cited by 18 | Viewed by 7498

Abstract

Here we propose the use of twist and glide symmetries to increase the equivalent refractive index in a helical guiding structure. Twist- and glide-symmetrical distributions are created with corrugations placed at both sides of a helical strip. Combined twist-and glide-symmetrical helical unit cells [...] Read more.

Here we propose the use of twist and glide symmetries to increase the equivalent refractive index in a helical guiding structure. Twist- and glide-symmetrical distributions are created with corrugations placed at both sides of a helical strip. Combined twist-and glide-symmetrical helical unit cells are studied in terms of their constituent parameters. The increase of the propagation constant is mainly controlled by the length of the corrugations. In our proposed helix antenna, twist and glide symmetry cells are used to reduce significantly the operational frequency compared with conventional helix antenna. Equivalently, for a given frequency of operation, the dimensions of helix are reduced with the use of higher symmetries. The theoretical results obtained for our proposed helical structure based on higher symmetries show a reduction of 42.2% in the antenna size maintaining a similar antenna performance when compared to conventional helix antennas. Full article

(This article belongs to the Special Issue Higher Symmetries and Its Application in Microwave Technology, Antennas and Metamaterials)

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25 pages, 1302 KiB

Open AccessEditor’s ChoiceArticle

Biological Bases of Beauty Revisited: The Effect of Symmetry, Averageness, and Sexual Dimorphism on Female Facial Attractiveness

by Alex L. Jones and Bastian Jaeger

Symmetry 2019, 11(2), 279; https://doi.org/10.3390/sym11020279 - 21 Feb 2019

Cited by 65 | Viewed by 20734

Abstract

The factors influencing human female facial attractiveness—symmetry, averageness, and sexual dimorphism—have been extensively studied. However, recent studies, using improved methodologies, have called into question their evolutionary utility and links with life history. The current studies use a range of approaches to quantify how [...] Read more.

The factors influencing human female facial attractiveness—symmetry, averageness, and sexual dimorphism—have been extensively studied. However, recent studies, using improved methodologies, have called into question their evolutionary utility and links with life history. The current studies use a range of approaches to quantify how important these factors actually are in perceiving attractiveness, through the use of novel statistical analyses and by addressing methodological weaknesses in the literature. Study One examines how manipulations of symmetry, averageness, femininity, and masculinity affect attractiveness using a two-alternative forced choice task, finding that increased masculinity and also femininity decrease attractiveness, compared to unmanipulated faces. Symmetry and averageness yielded a small and large effect, respectively. Study Two utilises a naturalistic ratings paradigm, finding similar effects of averageness and masculinity as Study One but no effects of symmetry and femininity on attractiveness. Study Three applies geometric face measurements of the factors and a random forest machine learning algorithm to predict perceived attractiveness, finding that shape averageness, dimorphism, and skin texture symmetry are useful features capable of relatively accurate predictions, while shape symmetry is uninformative. However, the factors do not explain as much variance in attractiveness as the literature suggests. The implications for future research on attractiveness are discussed. Full article

(This article belongs to the Special Issue Fluctuating asymmetry: A predictor of human life history outcomes)

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13 pages, 355 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nonclassical Symmetry Solutions for Non-Autonomous Reaction-Diffusion Equations

by Bronwyn H. Bradshaw-Hajek

Symmetry 2019, 11(2), 208; https://doi.org/10.3390/sym11020208 - 12 Feb 2019

Cited by 9 | Viewed by 3256

Abstract

The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the [...] Read more.

The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the reaction term are spatially dependent. We construct new exact group invariant solutions for several forms of the spatial dependence, and the relevance of some of the solutions to population dynamics modelling is discussed. Full article

(This article belongs to the Special Issue Lie Symmetries at Work in Biology and Medicine)

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34 pages, 2916 KiB

Open AccessEditor’s ChoiceArticle

Analysis of the Digital Divide Using Fuzzy Forecasting

by Paweł Ziemba and Jarosław Becker

Symmetry 2019, 11(2), 166; https://doi.org/10.3390/sym11020166 - 1 Feb 2019

Cited by 37 | Viewed by 4570

Abstract

In the countries of the former Eastern Bloc (Central and Eastern Europe) belonging to the European Union, a gradual elimination of the technological gap, greater expenditures, competitiveness and productivity can be noticed. In this context, analysis and forecast of the level of accessibility [...] Read more.

In the countries of the former Eastern Bloc (Central and Eastern Europe) belonging to the European Union, a gradual elimination of the technological gap, greater expenditures, competitiveness and productivity can be noticed. In this context, analysis and forecast of the level of accessibility and use of ICT (information and communication technologies) by households in these countries has become interesting. It allows for the selection of digitally excluded regions, or those threatened with this phenomenon in the coming years (2018–2020). To carry out the analysis, a framework based on fuzzy numbers and the NEAT F-PROMETHEE (New Easy Approach To Fuzzy-PROMETHEE) method was developed. The potential of the fuzzy outranking approach taking into account the uncertainty of input data (criteria and preferences) has been demonstrated as an alternative to the IDI (ICT Development Index) methodology widely used in research on regional ICT development based on composite indices. Research has shown that Estonia is the leader in the area of ICT expansion among households, and in the next three years will definitely maintain its dominant position. Slovenia follows shortly after, followed by Latvia. At the end of the ranking were the countries with the largest percentage in Central and Eastern Europe of population excluded digitally or threatened with this phenomenon; these are: Poland, Slovakia, Bulgaria and, in last place, Romania. Within this framework, the robustness of the obtained rankings to change in the degree of uncertainty of preferences was also examined. It turned out that eliminating the uncertainty of preferences resulted in an increase in the uncertainty of the aggregate, fuzzy grades obtained at the output. Full article

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

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18 pages, 391 KiB

Open AccessEditor’s ChoiceArticle

Spacetime Symmetry and LemaîTre Class Dark Energy Models

by Irina Dymnikova and Anna Dobosz

Symmetry 2019, 11(1), 90; https://doi.org/10.3390/sym11010090 - 15 Jan 2019

Cited by 6 | Viewed by 3390

Abstract

We present the regular cosmological models of the Lemaître class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame [...] Read more.

We present the regular cosmological models of the Lemaître class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame of one self-consistent theoretical scheme based on the algebraic classification of stress-energy tensors and spacetime symmetry directly related to their structure. Cosmological evolution starts with the nonsingular non-simultaneous de Sitter bang, followed by the Kasner-type anisotropic expansion, and goes towards the present de Sitter state. Spacetime symmetry provides a mechanism of reducing cosmological constant to a certain non-zero value involving the holographic principle which singles out the special class of the Lemaître dark energy models with the global structure of the de Sitter spacetime. For this class cosmological evolution is guided by quantum evaporation of the cosmological horizon whose dynamics entirely determines the final value of the cosmological constant. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale for the inflationary value of cosmological constant, its final value agrees with that given by observations. Anisotropy grows quickly at the postinflationary stage, then remains constant and decreases to

A < 10^{- 6}

when the vacuum density starts to dominate. Full article

(This article belongs to the Special Issue Cosmological Inflation, Dark Matter and Dark Energy)

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51 pages, 737 KiB

Open AccessEditor’s ChoiceArticle

Vacuum Condensate Picture of Quantum Gravity

by Herbert W. Hamber

Symmetry 2019, 11(1), 87; https://doi.org/10.3390/sym11010087 - 14 Jan 2019

Cited by 13 | Viewed by 3784

Abstract

In quantum gravity perturbation theory in Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the [...] Read more.

In quantum gravity perturbation theory in Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge–Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale

ξ

in many ways analogous to the scaling violation parameter

Λ_{\bar{M} S}

of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments. Full article

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

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