Symmetry

9 pages, 242 KiB

Open AccessArticle

Positive Solutions of a Fractional Thermostat Model with a Parameter

by Xinan Hao and Luyao Zhang

Symmetry 2019, 11(1), 122; https://doi.org/10.3390/sym11010122 - 21 Jan 2019

Cited by 14 | Viewed by 3380

We study the existence, multiplicity, and uniqueness results of positive solutions for a fractional thermostat model. Our approach depends on the fixed point index theory, iterative method, and nonsymmetry property of the Green function. The properties of positive solutions depending on a parameter [...] Read more.

We study the existence, multiplicity, and uniqueness results of positive solutions for a fractional thermostat model. Our approach depends on the fixed point index theory, iterative method, and nonsymmetry property of the Green function. The properties of positive solutions depending on a parameter are also discussed. Full article

(This article belongs to the Special Issue Fractional Differential Equations: Theory, Methods and Applications)

14 pages, 706 KiB

Open AccessArticle

The Existence of Symmetric Positive Solutions of Fourth-Order Elastic Beam Equations

by Münevver Tuz

Symmetry 2019, 11(1), 121; https://doi.org/10.3390/sym11010121 - 20 Jan 2019

Cited by 6 | Viewed by 3235

Abstract

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at [...] Read more.

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel’skii. Full article

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

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42 pages, 566 KiB

Open AccessArticle

Generating All 36,864 Four-Color Adinkras via Signed Permutations and Organizing into ℓ- and ℓ ˜ -Equivalence Classes

by S. James Gates, Jr., Kevin Iga, Lucas Kang, Vadim Korotkikh and Kory Stiffler

Symmetry 2019, 11(1), 120; https://doi.org/10.3390/sym11010120 - 20 Jan 2019

Cited by 7 | Viewed by 3672

Abstract

Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of

B C_{3}

, the signed permutation group of three [...] Read more.

Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of

B C_{3}

, the signed permutation group of three elements, and

B C_{4}

, the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via

B C_{4}

boson ×

B C_{3}

color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the gadget, which is used to distinguish adinkras. We show how 96 equivalence classes of adinkras that are based on the gadget emerge in terms of

B C_{3}

and

B C_{4}

. We also comment on the importance of the gadget as it relates to separating out dynamics in terms of Kähler-like potentials. Thus, on the basis of the complete analysis of the supersymmetrical representations achieved in the preparatory first four sections, the final comprehensive achievement of this work is the construction of the universal

B C_{4}

non-linear

σ

-model. Full article

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

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9 pages, 930 KiB

Open AccessArticle

Dynamics of Laterality in Lake Tanganyika Scale-Eaters Driven by Cross-Predation

by Michio Hori, Masanori Kohda, Satoshi Awata and Satoshi Takahashi

Symmetry 2019, 11(1), 119; https://doi.org/10.3390/sym11010119 - 20 Jan 2019

Cited by 2 | Viewed by 6803

Abstract

Scale-eating cichlid fishes, Perissodus spp., in Lake Tanganyika have laterally asymmetrical bodies, and each population is composed of righty and lefty morphs. Righty morphs attack the right side of prey and lefty morphs do the opposite. This anti-symmetric dimorphism has a genetic basis. [...] Read more.

Scale-eating cichlid fishes, Perissodus spp., in Lake Tanganyika have laterally asymmetrical bodies, and each population is composed of righty and lefty morphs. Righty morphs attack the right side of prey and lefty morphs do the opposite. This anti-symmetric dimorphism has a genetic basis. Temporal changes in the frequencies of morphs in two cohabiting scale-eating species (Perissodus microlepis and P. straeleni) were investigated over a 31-year period on a rocky shore at the southern end of the lake. Dimorphism was maintained dynamically during the period in both species, and the frequencies oscillated with a period of about four years in a semi-synchronized manner. Recent studies have indicated that this type of anti-symmetric dimorphism is shared widely among fishes, and is maintained by frequency-dependent selection between predator and prey species. The combinations of laterality in each scale-eater and its victim were surveyed. The results showed that “cross-predation”, in which righty predators catch lefty prey and lefty predators catch righty prey, occurred more frequently than the reverse combination (“parallel-predation”). The cause of the predominance of cross-predation is discussed from the viewpoint of the physical and sensory abilities of fishes. Full article

(This article belongs to the Special Issue Left Versus Right Asymmetries of Brain and Behaviour)

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11 pages, 1417 KiB

Open AccessArticle

Facility Location Problem Approach for Distributed Drones

by Jared Lynskey, Kyi Thar, Thant Zin Oo and Choong Seon Hong

Symmetry 2019, 11(1), 118; https://doi.org/10.3390/sym11010118 - 20 Jan 2019

Cited by 24 | Viewed by 5881

Abstract

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left [...] Read more.

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks. Full article

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

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16 pages, 312 KiB

Open AccessEditorial

Acknowledgement to Reviewers of Symmetry in 2018

by Symmetry Editorial Office

Symmetry 2019, 11(1), 117; https://doi.org/10.3390/sym11010117 - 19 Jan 2019

Viewed by 2887

Abstract

Rigorous peer-review is the corner-stone of high-quality academic publishing [...] Full article

20 pages, 367 KiB

Open AccessArticle

On a ℤ₂ⁿ-Graded Version of Supersymmetry

by Andrew James Bruce

Symmetry 2019, 11(1), 116; https://doi.org/10.3390/sym11010116 - 19 Jan 2019

Cited by 32 | Viewed by 3406

Abstract

We extend the notion of super-Minkowski space-time to include

Z_{2}^{n}

-graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical framework we employ is the recently developed category of [...] Read more.

We extend the notion of super-Minkowski space-time to include

Z_{2}^{n}

-graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical framework we employ is the recently developed category of

Z_{2}^{n}

-manifolds understood as locally ringed spaces. The formalism we present resembles

N

-extended superspace (in the presence of central charges), but with some subtle differences due to the exotic nature of the grading employed. Full article

16 pages, 3376 KiB

Open AccessArticle

MoSa: A Modeling and Sentiment Analysis System for Mobile Application Big Data

by Yaocheng Zhang, Wei Ren, Tianqing Zhu and Ehoche Faith

Symmetry 2019, 11(1), 115; https://doi.org/10.3390/sym11010115 - 19 Jan 2019

Cited by 11 | Viewed by 4224

Abstract

The development of mobile internet has led to a massive amount of data being generated from mobile devices daily, which has become a source for analyzing human behavior and trends in public sentiment. In this paper, we build a system called MoSa (Mobile [...] Read more.

The development of mobile internet has led to a massive amount of data being generated from mobile devices daily, which has become a source for analyzing human behavior and trends in public sentiment. In this paper, we build a system called MoSa (Mobile Sentiment analysis) to analyze this data. In this system, sentiment analysis is used to analyze news comments on the THAAD (Terminal High Altitude Area Defense) event from Toutiao by employing algorithms to calculate the sentiment value of the comment. This paper is based on HowNet; after the comparison of different sentiment dictionaries, we discover that the method proposed in this paper, which use a mixed sentiment dictionary, has a higher accuracy rate in its analysis of comment sentiment tendency. We then statistically analyze the relevant attributes of the comments and their sentiment values and discover that the standard deviation of the comments’ sentiment value can quickly reflect sentiment changes among the public. Besides that, we also derive some special models from the data that can reflect some specific characteristics. We find that the intrinsic characteristics of situational awareness have implicit symmetry. By using our system, people can obtain some practical results to guide interaction design in applications including mobile Internet, social networks, and blockchain based crowdsourcing. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Applications for Internet of Things Security and Privacy)

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7 pages, 234 KiB

Open AccessFeature PaperArticle

A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method

by Muhammad Aslam

Symmetry 2019, 11(1), 114; https://doi.org/10.3390/sym11010114 - 19 Jan 2019

Cited by 31 | Viewed by 3701

Abstract

The acceptance sampling plan plays an important role in maintaining the high quality of a product. The variable control chart, using classical statistics, helps in making acceptance or rejection decisions about the submitted lot of the product. Furthermore, the sampling plan, using classical [...] Read more.

The acceptance sampling plan plays an important role in maintaining the high quality of a product. The variable control chart, using classical statistics, helps in making acceptance or rejection decisions about the submitted lot of the product. Furthermore, the sampling plan, using classical statistics, assumes the complete or determinate information available about a lot of product. However, in some situations, data may be ambiguous, vague, imprecise, and incomplete or indeterminate. In this case, the use of neutrosophic statistics can be applied to guide the experimenters. In this paper, we originally proposed a new variable sampling plan using the neutrosophic interval statistical method. The neutrosophic operating characteristic (NOC) is derived using the neutrosophic normal distribution. The optimization solution is also presented for the proposed plan under the neutrosophic interval method. The effectiveness of the proposed plan is compared with the plan under classical statistics. The tables are presented for practical use and a real example is given to explain the neutrosophic fuzzy variable sampling plan in the industry. Full article

(This article belongs to the Special Issue New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications)

10 pages, 1787 KiB

Open AccessReview

Mathematical Modeling of Tissue Folding and Asymmetric Tissue Flow during Epithelial Morphogenesis

by Tetsuya Hiraiwa, Fu-Lai Wen, Tatsuo Shibata and Erina Kuranaga

Symmetry 2019, 11(1), 113; https://doi.org/10.3390/sym11010113 - 19 Jan 2019

Cited by 5 | Viewed by 5312

Abstract

Recent studies have revealed that intrinsic, individual cell behavior can provide the driving force for deforming a two-dimensional cell sheet to a three-dimensional tissue without the need for external regulatory elements. However, whether intrinsic, individual cell behavior could actually generate the force to [...] Read more.

Recent studies have revealed that intrinsic, individual cell behavior can provide the driving force for deforming a two-dimensional cell sheet to a three-dimensional tissue without the need for external regulatory elements. However, whether intrinsic, individual cell behavior could actually generate the force to induce tissue deformation was unclear, because there was no experimental method with which to verify it in vivo. In such cases, mathematical modeling can be effective for verifying whether a locally generated force can propagate through an entire tissue and induce deformation. Moreover, the mathematical model sometimes provides potential mechanistic insight beyond the information obtained from biological experimental results. Here, we present two examples of modeling tissue morphogenesis driven by cell deformation or cell interaction. In the first example, a mathematical study on tissue-autonomous folding based on a two-dimensional vertex model revealed that active modulations of cell mechanics along the basal–lateral surface, in addition to the apical side, can induce tissue-fold formation. In the second example, by applying a two-dimensional vertex model in an apical plane, a novel mechanism of tissue flow caused by asymmetric cell interactions was discovered, which explained the mechanics behind the collective cellular movement observed during epithelial morphogenesis. Full article

(This article belongs to the Special Issue Chiral Asymmetry in Cells)

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12 pages, 307 KiB

Open AccessArticle

by Xiangzhi Zhang and Yufeng Zhang

Symmetry 2019, 11(1), 112; https://doi.org/10.3390/sym11010112 - 18 Jan 2019

Cited by 8 | Viewed by 2718

Abstract

In the paper, we discuss some similarity solutions of the time-fractional Burgers system (TFBS). Firstly, with the help of the Lie-point symmetry and the corresponding invariant variables, we transform the TFBS to a fractional ordinary differential system (FODS) under the case where the [...] Read more.

In the paper, we discuss some similarity solutions of the time-fractional Burgers system (TFBS). Firstly, with the help of the Lie-point symmetry and the corresponding invariant variables, we transform the TFBS to a fractional ordinary differential system (FODS) under the case where the time-fractional derivative is the Riemann–Liouville type. The FODS can be approximated by some integer-order ordinary differential equations; here, we present three such integer-order ordinary differential equations (called IODE-1, IODE-2, and IODE-3, respectively). For IODE-1, we obtain its similarity solutions and numerical solutions, which approximate the similarity solutions and the numerical solutions of the TFBS. Secondly, we apply the numerical analysis method to obtain the numerical solutions of IODE-2 and IODE-3. Full article

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

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12 pages, 279 KiB

Open AccessFeature PaperArticle

Periodic Orbits of Third Kind in the Zonal J₂ + J₃ Problem

by M. Teresa de Bustos, Antonio Fernández, Miguel A. López, Raquel Martínez and Juan A. Vera

Symmetry 2019, 11(1), 111; https://doi.org/10.3390/sym11010111 - 18 Jan 2019

Cited by 1 | Viewed by 3010

Abstract

In this work, the periodic orbits’ phase portrait of the zonal

J_{2} + J_{3}

problem is studied. In particular, we center our attention on the periodic orbits of the third kind in the Poincaré sense using the averaging theory of dynamical [...] Read more.

In this work, the periodic orbits’ phase portrait of the zonal

J_{2} + J_{3}

problem is studied. In particular, we center our attention on the periodic orbits of the third kind in the Poincaré sense using the averaging theory of dynamical systems. We find three families of polar periodic orbits and four families of inclined periodic orbits for which we are able to state their explicit expressions. Full article

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

19 pages, 826 KiB

Open AccessArticle

A Robust Single-Valued Neutrosophic Soft Aggregation Operators in Multi-Criteria Decision Making

by Chiranjibe Jana and Madhumangal Pal

Symmetry 2019, 11(1), 110; https://doi.org/10.3390/sym11010110 - 18 Jan 2019

Cited by 82 | Viewed by 3890

Abstract

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object [...] Read more.

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object of this paper is to lay a foundation for providing a new approach of single-valued neutrosophic soft tool which is considering many problems that contain uncertainties. In present study, a new aggregation operators of single-valued neutrosophic soft numbers have so far not yet been applied for ranking of the alternatives in decision-making problems. To this propose work, single-valued neutrosophic soft weighted arithmetic averaging (SVNSWA) operator, single-valued neutrosophic soft weighted geometric averaging (SVNSWGA) operator have been used to compare two single-valued neutrosophic soft numbers (SVNSNs) for aggregating different single-valued neutrosophic soft input arguments in neutrosophic soft environment. Then, its related properties have been investigated. Finally, a practical example for Medical diagnosis problems provided to test the feasibility and applicability of the proposed work. Full article

(This article belongs to the Special Issue New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications)

2 pages, 143 KiB

Open AccessEditorial

Editorial of Special Issue “Information Technology and Its Applications”

by Tzu Chuen Lu

Symmetry 2019, 11(1), 109; https://doi.org/10.3390/sym11010109 - 18 Jan 2019

Cited by 1 | Viewed by 2092

Abstract

This book contains the successful invited submissions [...] Full article

(This article belongs to the Special Issue Information Technology and Its Applications)

15 pages, 367 KiB

Open AccessFeature PaperArticle

Singularities for One-Parameter Developable Surfaces of Curves

by Qiming Zhao, Donghe Pei and Yongqiao Wang

Symmetry 2019, 11(1), 108; https://doi.org/10.3390/sym11010108 - 17 Jan 2019

Cited by 8 | Viewed by 3017

Abstract

Developable surfaces, which are important objects of study, have attracted a lot of attention from many mathematicians. In this paper, we study the geometric properties of one-parameter developable surfaces associated with regular curves. According to singularity theory, the generic singularities of these developable [...] Read more.

Developable surfaces, which are important objects of study, have attracted a lot of attention from many mathematicians. In this paper, we study the geometric properties of one-parameter developable surfaces associated with regular curves. According to singularity theory, the generic singularities of these developable surfaces are classified—they are swallowtails and cuspidal edges. In addition, we give some examples of developable surfaces which have symmetric singularity models. Full article

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16 pages, 1697 KiB

Open AccessArticle

Visualization of High-Dimensional Data by Pairwise Fusion Matrices Using t-SNE

by Mujtaba Husnain, Malik Muhammad Saad Missen, Shahzad Mumtaz, Muhammad Muzzamil Luqman, Mickaël Coustaty and Jean-Marc Ogier

Symmetry 2019, 11(1), 107; https://doi.org/10.3390/sym11010107 - 17 Jan 2019

Cited by 25 | Viewed by 6644

Abstract

We applied t-distributed stochastic neighbor embedding (t-SNE) to visualize Urdu handwritten numerals (or digits). The data set used consists of 28 × 28 images of handwritten Urdu numerals. The data set was created by inviting authors from different categories of native Urdu speakers. [...] Read more.

We applied t-distributed stochastic neighbor embedding (t-SNE) to visualize Urdu handwritten numerals (or digits). The data set used consists of 28 × 28 images of handwritten Urdu numerals. The data set was created by inviting authors from different categories of native Urdu speakers. One of the challenging and critical issues for the correct visualization of Urdu numerals is shape similarity between some of the digits. This issue was resolved using t-SNE, by exploiting local and global structures of the large data set at different scales. The global structure consists of geometrical features and local structure is the pixel-based information for each class of Urdu digits. We introduce a novel approach that allows the fusion of these two independent spaces using Euclidean pairwise distances in a highly organized and principled way. The fusion matrix embedded with t-SNE helps to locate each data point in a two (or three-) dimensional map in a very different way. Furthermore, our proposed approach focuses on preserving the local structure of the high-dimensional data while mapping to a low-dimensional plane. The visualizations produced by t-SNE outperformed other classical techniques like principal component analysis (PCA) and auto-encoders (AE) on our handwritten Urdu numeral dataset. Full article

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16 pages, 1376 KiB

Open AccessArticle

Localized Fault Tolerant Algorithm Based on Node Movement Freedom Degree in Flying Ad Hoc Networks

by Qiang Guo, Jichen Yan and Wei Xu

Symmetry 2019, 11(1), 106; https://doi.org/10.3390/sym11010106 - 17 Jan 2019

Cited by 9 | Viewed by 3841

Abstract

Flying ad hoc network (FANET) is a communication network for data transmission among Unmanned Aerial Vehicles (UAVs). In ad hoc network, the UAVs movement is usually applied to improve network fault-tolerance, but it easily causes the disconnection of communication links, and the success [...] Read more.

Flying ad hoc network (FANET) is a communication network for data transmission among Unmanned Aerial Vehicles (UAVs). In ad hoc network, the UAVs movement is usually applied to improve network fault-tolerance, but it easily causes the disconnection of communication links, and the success rate is low. In this paper, we propose a local fault-tolerant control algorithm based on node movement freedom degree (LFTMF). Under the constraint of node movement freedom degree, the algorithm transforms the single-connected network into bi-connected network through the autonomous movement of UAVs to improve the fault-tolerant ability of the FANET network. Firstly, the consistency between k-hop cut-points and global cut-points in FANET network is analyzed. Then, based on the k-hop local topology of FANET network, the UAV node movement freedom degree model is established. Finally, according to the location distribution of k-hop cut-points in the FANET network, the bi-connected fault-tolerant network is realized by UAVs cascade movement. Compared with the existing algorithms, simulation results show that the proposed algorithm achieves better performance in success rate, deviation distance, cascade movement ratio and adjustment period. Full article

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9 pages, 258 KiB

Open AccessArticle

Some Results on the Symmetric Representation of the Generalized Drazin Inverse in a Banach Algebra

by Yonghui Qin, Xiaoji Liu and Julio Benítez

Symmetry 2019, 11(1), 105; https://doi.org/10.3390/sym11010105 - 17 Jan 2019

Cited by 4 | Viewed by 2842

Abstract

Based on the conditions

a b^{2} = 0

and

b^{π} (a b) \in A^{d}

, we derive that

{(a b)}^{n}

,

{(b a)}^{n}

, and

a b + b a

are all [...] Read more.

Based on the conditions

a b^{2} = 0

and

b^{π} (a b) \in A^{d}

, we derive that

{(a b)}^{n}

,

{(b a)}^{n}

, and

a b + b a

are all generalized Drazin invertible in a Banach algebra

A

, where

n \in N

and a and b are elements of

A

. By using these results, some results on the symmetry representations for the generalized Drazin inverse of

a b + b a

are given. We also consider that additive properties for the generalized Drazin inverse of the sum

a + b

. Full article

(This article belongs to the Special Issue Matrices and Symmetry)

29 pages, 9021 KiB

Open AccessFeature PaperArticle

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

by Dmitry Kazakov, Leonid Bork, Arthur Borlakov, Denis Tolkachev and Dmitry Vlasenko

Symmetry 2019, 11(1), 104; https://doi.org/10.3390/sym11010104 - 17 Jan 2019

Cited by 4 | Viewed by 2913

Abstract

Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions, they are free from UV divergences but are IR divergent on shell; in higher dimensions, on the contrary, they are IR finite but [...] Read more.

Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions, they are free from UV divergences but are IR divergent on shell; in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows, we consider the four-point on-shell scattering amplitudes in

D = 6, 8, 10

supersymmetric Yang–Mills theory in the planar limit within the spinor-helicity and on-shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the

R

-operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure, which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behavior and find that, while each term of PT increases as a power of energy, the total sum behaves differently: in

D = 6

two partial amplitudes decrease with energy and the third one increases exponentially, while in

D = 8

and 10 the amplitudes possess an infinite number of periodic poles at finite energy. Full article

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

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13 pages, 327 KiB

Open AccessArticle

Local Convergence of a Family of Weighted-Newton Methods

by Ramandeep Behl, Ioannis K. Argyros, J.A. Tenreiro Machado and Ali Saleh Alshomrani

Symmetry 2019, 11(1), 103; https://doi.org/10.3390/sym11010103 - 17 Jan 2019

Cited by 1 | Viewed by 2848

Abstract

This article considers the fourth-order family of weighted-Newton methods. It provides the range of initial guesses that ensure the convergence. The analysis is given for Banach space-valued mappings, and the hypotheses involve the derivative of order one. The convergence radius, error estimations, and [...] Read more.

This article considers the fourth-order family of weighted-Newton methods. It provides the range of initial guesses that ensure the convergence. The analysis is given for Banach space-valued mappings, and the hypotheses involve the derivative of order one. The convergence radius, error estimations, and results on uniqueness also depend on this derivative. The scope of application of the method is extended, since no derivatives of higher order are required as in previous works. Finally, we demonstrate the applicability of the proposed method in real-life problems and discuss a case where previous studies cannot be adopted. Full article

(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)

11 pages, 3517 KiB

Open AccessArticle

A Novel 2D—Grid of Scroll Chaotic Attractor Generated by CNN

by Ahmed M. Ali, Saif M. Ramadhan and Fadhil R. Tahir

Symmetry 2019, 11(1), 99; https://doi.org/10.3390/sym11010099 - 16 Jan 2019

Cited by 6 | Viewed by 4787

Abstract

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and [...] Read more.

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line

x = y

has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (

1 \times 3

) cells. The paper concerns on the design and implementation of

2 \times 2

and

3 \times 3

2 D

-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice. Full article

(This article belongs to the Special Issue Nonlinear Circuits and Systems in Symmetry)

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13 pages, 2279 KiB

Open AccessArticle

The Two Supreme Principles of Plato’s Cosmos—the One and the Indefinite Dyad—the Division of a Straight Line into Extreme and Mean Ratio, and Pingala’s Mātrāmeru

by Maria Antonietta Salamone

Symmetry 2019, 11(1), 98; https://doi.org/10.3390/sym11010098 - 16 Jan 2019

Cited by 2 | Viewed by 7995

Abstract

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. [...] Read more.

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a–b, Plato uses Pingala’s Mātrāmeru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the point of identifying the two supreme principles of the Cosmos—the One (1) and the Indefinite Dyad (Φ and1/Φ)—with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = Φ) and the Mātrāmeru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible. Full article

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15 pages, 3735 KiB

Open AccessArticle

Symmetric Magnetic Anomaly Objects’ Orientation Recognition Based on Local Binary Pattern and Support Vector Machine

by Jianyong Zheng, Hongbo Fan, Zhining Li and Qi Zhang

Symmetry 2019, 11(1), 97; https://doi.org/10.3390/sym11010097 - 16 Jan 2019

Cited by 2 | Viewed by 3527

Abstract

In order to identify the orientation or recognize the attitude of small symmetric magnetic anomaly objects at shallow depth, we propose a method of extracting local binary pattern (LBP) features from denoised magnetic anomaly signals and classifying symmetric magnetic objects that have different [...] Read more.

In order to identify the orientation or recognize the attitude of small symmetric magnetic anomaly objects at shallow depth, we propose a method of extracting local binary pattern (LBP) features from denoised magnetic anomaly signals and classifying symmetric magnetic objects that have different orientations based on support vector machine (SVM). First, nine component signals, such as magnetic gradient tensor matrix, total magnetic intensity (TMI), and so forth, are calculated from the original signal detected by the flux gate sensors. The nine component signals are processed by discrete wavelet transform (DWT), which aims to reduce noise and make the signal’s features clear. Then we extract LBP texture features from the denoised nine component signals. From the simulation analysis, we can conclude that the LBP texture features of the nine component signals have good interclass discrimination and intraclass aggregation, which can be used for pattern recognition. Finally, the LBP texture features are constructed into feature vectors. The orientations of symmetric ferromagnetic objects underground are identified by SVM based on the feature vectors. Through experiments, we can conclude that the orientation recognition accuracy rate reaches 90%. This suggests that we can obtain the details of magnetic anomalies through our method. Full article

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11 pages, 470 KiB

Open AccessArticle

Symmetric Face Normalization

by Ya Su, Zhe Liu and Xiaojuan Ban

Symmetry 2019, 11(1), 96; https://doi.org/10.3390/sym11010096 - 16 Jan 2019

Cited by 5 | Viewed by 3559

Abstract

Image registration is an important process in image processing which is used to improve the performance of computer vision related tasks. In this paper, a novel self-registration method, namely symmetric face normalization (SFN) algorithm, is proposed. There are three contributions in this paper. [...] Read more.

Image registration is an important process in image processing which is used to improve the performance of computer vision related tasks. In this paper, a novel self-registration method, namely symmetric face normalization (SFN) algorithm, is proposed. There are three contributions in this paper. Firstly, a self-normalization algorithm for face images is proposed, which normalizes a face image to be reflection symmetric horizontally. It has the advantage that no face model needs to be built, which is always severely time-consuming. Moreover, it can be considered as a pre-processing procedure which greatly decreases the parameters needed to be adjusted. Secondly, an iterative algorithm is designed to solve the self-normalization algorithm. Finally, SFN is applied to the between-image alignment problem, which results in the symmetric face alignment (SFA) algorithm. Experiments performed on face databases show that the accuracy of SFN is higher than 0.95 when the translation on the x-axis is lower than 15 pixels, or the rotation angle is lower than 18°. Moreover, the proposed SFA outperforms the state-of-the-art between-image alignment algorithm in efficiency (about four times) without loss of accuracy. Full article

(This article belongs to the Special Issue Symmetry in Cooperative Applications III)

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20 pages, 12243 KiB

Open AccessArticle

No-Reference Image Quality Assessment with Local Gradient Orientations

by Mariusz Oszust

Symmetry 2019, 11(1), 95; https://doi.org/10.3390/sym11010095 - 16 Jan 2019

Cited by 10 | Viewed by 4503

Abstract

Image processing methods often introduce distortions, which affect the way an image is subjectively perceived by a human observer. To avoid inconvenient subjective tests in cases in which reference images are not available, it is desirable to develop an automatic no-reference image quality [...] Read more.

Image processing methods often introduce distortions, which affect the way an image is subjectively perceived by a human observer. To avoid inconvenient subjective tests in cases in which reference images are not available, it is desirable to develop an automatic no-reference image quality assessment (NR-IQA) technique. In this paper, a novel NR-IQA technique is proposed in which the distributions of local gradient orientations in image regions of different sizes are used to characterize an image. To evaluate the objective quality of an image, its luminance and chrominance channels are processed, as well as their high-order derivatives. Finally, statistics of used perceptual features are mapped to subjective scores by the support vector regression (SVR) technique. The extensive experimental evaluation on six popular IQA benchmark datasets reveals that the proposed technique is highly correlated with subjective scores and outperforms related state-of-the-art hand-crafted and deep learning approaches. Full article

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20 pages, 1861 KiB

Open AccessArticle

Improving Accuracy of the Kalman Filter Algorithm in Dynamic Conditions Using ANN-Based Learning Module

by Israr Ullah, Muhammad Fayaz and DoHyeun Kim

Symmetry 2019, 11(1), 94; https://doi.org/10.3390/sym11010094 - 16 Jan 2019

Cited by 37 | Viewed by 7744

Abstract

Prediction algorithms enable computers to learn from historical data in order to make accurate decisions about an uncertain future to maximize expected benefit or avoid potential loss. Conventional prediction algorithms are usually based on a trained model, which is learned from historical data. [...] Read more.

Prediction algorithms enable computers to learn from historical data in order to make accurate decisions about an uncertain future to maximize expected benefit or avoid potential loss. Conventional prediction algorithms are usually based on a trained model, which is learned from historical data. However, the problem with such prediction algorithms is their inability to adapt to dynamic scenarios and changing conditions. This paper presents a novel learning to prediction model to improve the performance of prediction algorithms under dynamic conditions. In the proposed model, a learning module is attached to the prediction algorithm, which acts as a supervisor to monitor and improve the performance of the prediction algorithm continuously by analyzing its output and considering external factors that may have an influence on its performance. To evaluate the effectiveness of the proposed learning to prediction model, we have developed the artificial neural network (ANN)-based learning module to improve the prediction accuracy of the Kalman filter algorithm as a case study. For experimental analysis, we consider a scenario where the Kalman filter algorithm is used to predict actual temperature from noisy sensor readings. the Kalman filter algorithm uses fixed process error covariance R, which is not suitable for dynamic situations where the error in sensor readings varies due to some external factors. In this study, we assume variable error in temperature sensor readings due to the changing humidity level. We have developed a learning module based on ANN to estimate the amount of error in current readings and to update R in the Kalman filter accordingly. Through experiments, we observed that the Kalman filter with the learning module performed better (4.41%–11.19%) than the conventional Kalman filter algorithm in terms of the root mean squared error metric. Full article

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20 pages, 4041 KiB

Open AccessFeature PaperReview

Chiral Neuronal Motility: The Missing Link between Molecular Chirality and Brain Asymmetry

by Atsushi Tamada

Symmetry 2019, 11(1), 102; https://doi.org/10.3390/sym11010102 - 16 Jan 2019

Cited by 12 | Viewed by 8293

Abstract

Left–right brain asymmetry is a fundamental property observed across phyla from invertebrates to humans, but the mechanisms underlying its formation are still largely unknown. Rapid progress in our knowledge of the formation of body asymmetry suggests that brain asymmetry might be controlled by [...] Read more.

Left–right brain asymmetry is a fundamental property observed across phyla from invertebrates to humans, but the mechanisms underlying its formation are still largely unknown. Rapid progress in our knowledge of the formation of body asymmetry suggests that brain asymmetry might be controlled by the same mechanisms. However, most of the functional brain laterality, including language processing and handedness, does not share common mechanisms with visceral asymmetry. Accumulating evidence indicates that asymmetry is manifested as chirality at the single cellular level. In neurons, the growth cone filopodia at the tips of neurites exhibit a myosin V-dependent, left-helical, and right-screw rotation, which drives the clockwise circular growth of neurites on adhesive substrates. Here, I propose an alternative model for the formation of brain asymmetry that is based on chiral neuronal motility. According to this chiral neuron model, the molecular chirality of actin filaments and myosin motors is converted into chiral neuronal motility, which is in turn transformed into the left–right asymmetry of neural circuits and lateralized brain functions. I also introduce automated, numerical, and quantitative methods to analyze the chirality and the left–right asymmetry that would enable the efficient testing of the model and to accelerate future investigations in this field. Full article

(This article belongs to the Special Issue Chiral Asymmetry in Cells)

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14 pages, 4165 KiB

Open AccessArticle

Inspired by Human Eye: Vestibular Ocular Reflex Based Gimbal Camera Movement to Minimize Viewpoint Changes

by Adithya B., Pavan Kumar B. N., Young Ho Chai and Ashok Kumar Patil

Symmetry 2019, 11(1), 101; https://doi.org/10.3390/sym11010101 - 16 Jan 2019

Cited by 6 | Viewed by 5850

Abstract

Human eyeballs move relative to the head, resulting in optimal changes in the viewpoint. We tested similar vestibular ocular reflex (VOR)-based movement on Zenmuse-X3 gimbal camera relative to pre-defined YAW movements of the DJI Matrice-100 unmanned aerial vehicle (UAV). Changes in viewpoint have [...] Read more.

Human eyeballs move relative to the head, resulting in optimal changes in the viewpoint. We tested similar vestibular ocular reflex (VOR)-based movement on Zenmuse-X3 gimbal camera relative to pre-defined YAW movements of the DJI Matrice-100 unmanned aerial vehicle (UAV). Changes in viewpoint have various consequences for visual and graphical rendering. Therefore, this study investigated how to minimize these changes. OpenGL visualization was performed to simulate and measure viewpoint changes using the proposed VOR-based eyeball movement algorithm and compared with results of VOR based gimbal movement. The gimbal camera was setup to render images (scenes) on flat monitors. Positions of pre-fixed targets in the images were used to measure the viewpoint changes. The proposed approach could successfully control and significantly reduce the viewpoint changes and stabilize the image to improve visual tracking of targets on flat monitors. The proposed method can also be used to render real-time camera feed to a head-mounted display (HMD) in an ergonomically pleasing way. Full article

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10 pages, 265 KiB

Open AccessArticle

Breakable Semihypergroups

by Dariush Heidari and Irina Cristea

Symmetry 2019, 11(1), 100; https://doi.org/10.3390/sym11010100 - 16 Jan 2019

Cited by 11 | Viewed by 3588

Abstract

In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric [...] Read more.

In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups. Full article

(This article belongs to the Special Issue Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures)

20 pages, 338 KiB

Open AccessArticle

Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

by Zhenhua Ma, Azhar Hussain, Muhammad Adeel, Nawab Hussain and Ekrem Savas

Symmetry 2019, 11(1), 93; https://doi.org/10.3390/sym11010093 - 15 Jan 2019

Cited by 5 | Viewed by 3790

Abstract

In this paper, we introduce the notion of

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α

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ψ

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Θ

-contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially [...] Read more.

In this paper, we introduce the notion of

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iri

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type

α

-

ψ

-

Θ

-contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation

X = Q + \sum_{i = 1}^{m} A_{i}^{*} γ (X) A_{i}

and give a numerical example. Full article

(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)

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Symmetry, Volume 11, Issue 1 (January 2019) – 122 articles

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