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Symmetry, Volume 7, Issue 3 (September 2015) – 25 articles , Pages 1151-1669

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Article
An Elementary Derivation of the Matrix Elements of Real Irreducible Representations of so(3)
Symmetry 2015, 7(3), 1655-1669; https://doi.org/10.3390/sym7031655 - 14 Sep 2015
Cited by 5 | Viewed by 2024
Abstract
Using elementary techniques, an algorithmic procedure to construct skew-symmetric matrices realizing the real irreducible representations of so(3) is developed. We further give a simple criterion that enables one to deduce the decomposition of an arbitrary real representation R of so(3) into real irreducible [...] Read more.
Using elementary techniques, an algorithmic procedure to construct skew-symmetric matrices realizing the real irreducible representations of so(3) is developed. We further give a simple criterion that enables one to deduce the decomposition of an arbitrary real representation R of so(3) into real irreducible components from the characteristic polynomial of an arbitrary representation matrix. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
Article
Uncertainty Analysis of 208Pb Neutron Skin Predictions with Chiral Interactions
Symmetry 2015, 7(3), 1646-1654; https://doi.org/10.3390/sym7031646 - 14 Sep 2015
Cited by 3 | Viewed by 2081
Abstract
We report predictions for the neutron skin in 208Pb using chiral two- and three-body interactions at increasing orders of chiral effective field theory and varying resolution scales. Closely related quantities, such as the slope of the symmetry energy, are also discussed. The [...] Read more.
We report predictions for the neutron skin in 208Pb using chiral two- and three-body interactions at increasing orders of chiral effective field theory and varying resolution scales. Closely related quantities, such as the slope of the symmetry energy, are also discussed. The sensitivity of the skin to just pure neutron matter pressure when going from order 2 to order 4 of chiral effective theory is singled out in a set of calculations that employ an empirical equation of state for symmetric nuclear matter. Full article
(This article belongs to the Special Issue Symmetry in Hadrons and Nuclei)
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Article
Mirror Symmetry and Polar Duality of Polytopes
Symmetry 2015, 7(3), 1633-1645; https://doi.org/10.3390/sym7031633 - 10 Sep 2015
Cited by 5 | Viewed by 2978
Abstract
This expository article explores the connection between the polar duality from polyhedral geometry and mirror symmetry from mathematical physics and algebraic geometry. Topics discussed include duality of polytopes and cones as well as the famous quintic threefold and the toric variety of a [...] Read more.
This expository article explores the connection between the polar duality from polyhedral geometry and mirror symmetry from mathematical physics and algebraic geometry. Topics discussed include duality of polytopes and cones as well as the famous quintic threefold and the toric variety of a reflexive polytope. Full article
(This article belongs to the Special Issue Symmetry and Duality)
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Article
Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model
Symmetry 2015, 7(3), 1613-1632; https://doi.org/10.3390/sym7031613 - 08 Sep 2015
Cited by 14 | Viewed by 2836
Abstract
Basener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the [...] Read more.
Basener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the involved parameters satisfy certain relationships. We have also discerned hidden linearity. Moreover, we have determined a Jacobi last multiplier and, consequently, a Lagrangian for the general system and have found other cases independently and dependently on symmetry considerations in order to construct a corresponding variational problem, thus enabling us to find conservation laws by means of Noether’s theorem. A comparison with the qualitative analysis given by Basener and Ross is provided. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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Article
From Conformal Invariance towards Dynamical Symmetries of the Collisionless Boltzmann Equation
Symmetry 2015, 7(3), 1595-1612; https://doi.org/10.3390/sym7031595 - 07 Sep 2015
Cited by 11 | Viewed by 2123
Abstract
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the 2D conformal algebra. In the case without external forces, the symmetry of the conformally-invariant transport equation [...] Read more.
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the 2D conformal algebra. In the case without external forces, the symmetry of the conformally-invariant transport equation is first generalized by considering the particle momentum as an independent variable. This new conformal representation can be further extended to include an external force. The construction and possible physical applications are outlined. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
Article
Prevention of Exponential Equivalence in Simple Password Exponential Key Exchange (SPEKE)
Symmetry 2015, 7(3), 1587-1594; https://doi.org/10.3390/sym7031587 - 02 Sep 2015
Cited by 2 | Viewed by 1951
Abstract
Simple Password Exponential Key Exchange (SPEKE) and Dragonfly are simple password-based authenticated key exchange protocols that use a value derived from a shared password as a generator for modular exponentiation, as opposed to Diffie–Hellman key exchange, which uses a fixed value. However, it [...] Read more.
Simple Password Exponential Key Exchange (SPEKE) and Dragonfly are simple password-based authenticated key exchange protocols that use a value derived from a shared password as a generator for modular exponentiation, as opposed to Diffie–Hellman key exchange, which uses a fixed value. However, it has been shown that in SPEKE, an active attacker, can examine multiple passwords in a single attempt because the passwords have an exponential correlation.We show that Dragonfly can also suffer from the same problem, and we propose a simple countermeasure to prevent the exponential equivalence in SPEKE. Full article
Article
Design of IP Camera Access Control Protocol by Utilizing Hierarchical Group Key
Symmetry 2015, 7(3), 1567-1586; https://doi.org/10.3390/sym7031567 - 27 Aug 2015
Cited by 7 | Viewed by 4635
Abstract
Unlike CCTV, security video surveillance devices, which we have generally known about, IP cameras which are connected to a network either with or without wire, provide monitoring services through a built-in web-server. Due to the fact that IP cameras can use a network [...] Read more.
Unlike CCTV, security video surveillance devices, which we have generally known about, IP cameras which are connected to a network either with or without wire, provide monitoring services through a built-in web-server. Due to the fact that IP cameras can use a network such as the Internet, multiple IP cameras can be installed at a long distance and each IP camera can utilize the function of a web server individually. Even though IP cameras have this kind of advantage, it has difficulties in access control management and weakness in user certification, too. Particularly, because the market of IP cameras did not begin to be realized a long while ago, systems which are systematized from the perspective of security have not been built up yet. Additionally, it contains severe weaknesses in terms of access authority to the IP camera web server, certification of users, and certification of IP cameras which are newly installed within a network, etc. This research grouped IP cameras hierarchically to manage them systematically, and provided access control and data confidentiality between groups by utilizing group keys. In addition, IP cameras and users are certified by using PKI-based certification, and weak points of security such as confidentiality and integrity, etc., are improved by encrypting passwords. Thus, this research presents specific protocols of the entire process and proved through experiments that this method can be actually applied. Full article
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Article
Lie Symmetry Analysis of the Hopf Functional-Differential Equation
Symmetry 2015, 7(3), 1536-1566; https://doi.org/10.3390/sym7031536 - 27 Aug 2015
Cited by 6 | Viewed by 2986
Abstract
In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie [...] Read more.
In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extended Lie symmetry analysis in the physical space where we have to deal with the transformation of the integration variable in the appearing integral terms. The method is based on the transformation of the product y(x)dx appearing in the integral terms and applied to the functional formulation of the viscous Burgers equation. The extended Lie symmetry analysis furnishes all known symmetries of the viscous Burgers equation and is able to provide new symmetries associated with the Hopf formulation of the viscous Burgers equation. Hence, it can be employed as an important tool for applications in continuum mechanics. Full article
Review
Enantioselective Organocatalyzed Synthesis of 2-Amino-3-cyano-4H-chromene Derivatives
Symmetry 2015, 7(3), 1519-1535; https://doi.org/10.3390/sym7031519 - 26 Aug 2015
Cited by 22 | Viewed by 4649
Abstract
The structural motif that results from the fusion of a benzene ring to a heterocyclic pyran ring, known as chromene, is broadly found in nature and it has been reported to be associated with a wide range of biological activity. Moreover, asymmetric organocatalysis [...] Read more.
The structural motif that results from the fusion of a benzene ring to a heterocyclic pyran ring, known as chromene, is broadly found in nature and it has been reported to be associated with a wide range of biological activity. Moreover, asymmetric organocatalysis is a discipline in expansion that is already recognized as a well-established tool for obtaining enantiomerically enriched compounds. This review covers the particular case of the asymmetric synthesis of 2-amino-3-cyano-4H-chromenes using organocatalysis. Herein, we show the most illustrative examples of the methods developed by diverse research groups, following a classification based on these five different approaches: (1) addition of naphthol compounds to substituted α,α-dicyanoolefins; (2) addition of malononitrile to substituted o-vinylphenols; (3) addition of malononitrile to N-protected o-iminophenols; (4) Michael addition of nucleophiles to 2-iminochromene derivatives; and (5) organocatalyzed formal [4+2] cycloaddition reaction. In most cases, chiral thioureas have been found to be effective catalysts to promote the synthetic processes, and generally a bifunctional mode of action has been envisioned for them. In addition, squaramides and cinchona derivatives have been occasionally used as suitable catalysts for the substrates activation. Full article
(This article belongs to the Special Issue Asymmetric Catalysis)
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Article
Performance Enhancement of Face Recognition in Smart TV Using Symmetrical Fuzzy-Based Quality Assessment
Symmetry 2015, 7(3), 1475-1518; https://doi.org/10.3390/sym7031475 - 25 Aug 2015
Cited by 4 | Viewed by 3099
Abstract
With the rapid growth of smart TV, the necessity for recognizing a viewer has increased for various applications that deploy face recognition to provide intelligent services and high convenience to viewers. However, the viewers can have various postures, illumination, and expression variations on [...] Read more.
With the rapid growth of smart TV, the necessity for recognizing a viewer has increased for various applications that deploy face recognition to provide intelligent services and high convenience to viewers. However, the viewers can have various postures, illumination, and expression variations on their faces while watching TV, and thereby, the performance of face recognition inevitably degrades. In order to handle these problems, video-based face recognition has been proposed, instead of a single image-based one. However, video-based processing of multiple images is prohibitive in smart TVs as the processing power is limited. Therefore, a quality measure-based (QM-based) image selection is required that considers both the processing speed and accuracy of face recognition. Therefore, we propose a performance enhancement method for face recognition through symmetrical fuzzy-based quality assessment. Our research is novel in the following three ways as compared to previous works. First, QMs are adaptively selected by comparing variance values obtained from candidate QMs within a video sequence, where the higher the variance value by a QM, the more meaningful is the QM in terms of a distinction between images. Therefore, we can adaptively select meaningful QMs that reflect the primary factors influencing the performance of face recognition. Second, a quality score of an image is calculated using a fuzzy method based on the inputs of the selected QMs, symmetrical membership functions, and rule table considering the characteristics of symmetry. A fuzzy-based combination method of image quality has the advantage of being less affected by the types of face databases because it does not perform an additional training procedure. Third, the accuracy of face recognition is enhanced by fusing the matching scores of the high-quality face images, which are selected based on the quality scores among successive face mages. Experimental results showed that the performance of face recognition using the proposed method was better than that of conventional methods in terms of accuracy. Full article
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Article
A (1+2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions
Symmetry 2015, 7(3), 1463-1474; https://doi.org/10.3390/sym7031463 - 24 Aug 2015
Cited by 6 | Viewed by 2388
Abstract
This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible [...] Read more.
This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller–Segel system in question were found. Lie symmetry operators are used for constructing exact solutions of some boundary value problems. Moreover, it is proved that the boundary value problem for the (1+1)-dimensional Keller–Segel system with specific boundary conditions can be linearized and solved in an explicit form. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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Technical Note
Estrada and L-Estrada Indices of Edge-Independent Random Graphs
Symmetry 2015, 7(3), 1455-1462; https://doi.org/10.3390/sym7031455 - 19 Aug 2015
Cited by 14 | Viewed by 2273
Abstract
Let \(G\) be a simple graph of order \(n\) with eigenvalues \(\lambda_1,\lambda_2,\cdots,\lambda_n\) and normalized Laplacian eigenvalues \(\mu_1,\mu_2,\cdots,\mu_n\). The Estrada index and normalized Laplacian Estrada index are defined as \(EE(G)=\sum_{k=1}^ne^{\lambda_k}\) and \(\mathcal{L}EE(G)=\sum_{k=1}^ne^{\mu_k-1}\), respectively. We establish upper and lower bounds to \(EE\) and \(\mathcal{L}EE\) for [...] Read more.
Let \(G\) be a simple graph of order \(n\) with eigenvalues \(\lambda_1,\lambda_2,\cdots,\lambda_n\) and normalized Laplacian eigenvalues \(\mu_1,\mu_2,\cdots,\mu_n\). The Estrada index and normalized Laplacian Estrada index are defined as \(EE(G)=\sum_{k=1}^ne^{\lambda_k}\) and \(\mathcal{L}EE(G)=\sum_{k=1}^ne^{\mu_k-1}\), respectively. We establish upper and lower bounds to \(EE\) and \(\mathcal{L}EE\) for edge-independent random graphs, containing the classical Erdös-Rényi graphs as special cases. Full article
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Article
Asymmetry Assessment Using Surface Topography in Healthy Adolescents
Symmetry 2015, 7(3), 1436-1454; https://doi.org/10.3390/sym7031436 - 17 Aug 2015
Cited by 7 | Viewed by 3399
Abstract
The ability to assess geometric asymmetry in the torsos of individuals is important for detecting Adolescent Idiopathic Scoliosis (AIS). A markerless technique using Surface Topography (ST) has been introduced as a non-invasive alternative to standard diagnostic radiographs. The technique has been used to [...] Read more.
The ability to assess geometric asymmetry in the torsos of individuals is important for detecting Adolescent Idiopathic Scoliosis (AIS). A markerless technique using Surface Topography (ST) has been introduced as a non-invasive alternative to standard diagnostic radiographs. The technique has been used to identify asymmetry patterns associated with AIS. However, the presence and nature of asymmetries in the healthy population has not been properly studied. The purpose of this study is therefore to identify asymmetries and potential relationships to development factors such as age, gender, hand dominance and unilateral physical activity in healthy adolescents. Full torso scans of 83 participants were analyzed. Using Geomagic, deviation contour maps (DCMs) were created by reflecting the torso along the best plane of sagittal symmetry with each spectrum normalized. Two classes of asymmetry were observed: twist and thickness each with subgroupings. Averaged interobserver and intraobserver Kappas for twist subgroupings were 0.84 and 0.84, respectively, and for thickness subgroupings were 0.53 and 0.63 respectively. Further significant relationships were observed between specific types of asymmetry and gender such as females displaying predominately twist asymmetry, and males with thickness asymmetry. However, no relationships were found between type of asymmetry and age, hand dominance or unilateral physical activity. Understanding asymmetries in healthy subjects will continue to enhance assessment ability of the markerless ST technique. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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Article
Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2)-Dimensional Boundary Value Problems
Symmetry 2015, 7(3), 1410-1435; https://doi.org/10.3390/sym7031410 - 17 Aug 2015
Cited by 14 | Viewed by 2665
Abstract
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary [...] Read more.
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direct applicability to the nonlinear problems arising in applications are demonstrated. Moreover, the successful application of the definition for the Lie and conditional symmetry classification of a class of (1 + 2)-dimensional nonlinear boundary value problems governed by the nonlinear diffusion equation in a semi-infinite domain is realised. In particular, it is proven that there is a special exponent, k ≠ -2, for the power diffusivity uk when the problem in question with non-vanishing flux on the boundary admits additional Lie symmetry operators compared to the case k ≠ -2. In order to demonstrate the applicability of the symmetries derived, they are used for reducing the nonlinear problems with power diffusivity uk and a constant non-zero flux on the boundary (such problems are common in applications and describing a wide range of phenomena) to (1 + 1)-dimensional problems. The structure and properties of the problems obtained are briefly analysed. Finally, some results demonstrating how Lie invariance of the boundary value problem in question depends on the geometry of the domain are presented. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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Article
Enantioselective Organocatalysis in Microreactors: Continuous Flow Synthesis of a (S)-Pregabalin Precursor and (S)-Warfarin
Symmetry 2015, 7(3), 1395-1409; https://doi.org/10.3390/sym7031395 - 04 Aug 2015
Cited by 28 | Viewed by 4609
Abstract
Continuous flow processes have recently emerged as a powerful technology for performing chemical transformations since they ensure some advantages over traditional batch procedures. In this work, the use of commercially available and affordable PEEK (Polyetheretherketone) and PTFE (Polytetrafluoroethylene) HPLC (High Performance Liquid Chromatography) [...] Read more.
Continuous flow processes have recently emerged as a powerful technology for performing chemical transformations since they ensure some advantages over traditional batch procedures. In this work, the use of commercially available and affordable PEEK (Polyetheretherketone) and PTFE (Polytetrafluoroethylene) HPLC (High Performance Liquid Chromatography) tubing as microreactors was exploited to perform organic reactions under continuous flow conditions, as an alternative to the commercial traditional glass microreactors. The wide availability of tubing with different sizes allowed quickly running small-scale preliminary screenings, in order to optimize the reaction parameters, and then to realize under the best experimental conditions a reaction scale up for preparative purposes. The gram production of some Active Pharmaceutical Ingredients (APIs) such as (S)-Pregabalin and (S)-Warfarin was accomplished in short reaction time with high enantioselectivity, in an experimentally very simple procedure. Full article
(This article belongs to the Special Issue Asymmetric Catalysis)
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Article
Bäcklund Transformations for Integrable Geometric Curve Flows
Symmetry 2015, 7(3), 1376-1394; https://doi.org/10.3390/sym7031376 - 03 Aug 2015
Cited by 6 | Viewed by 2480
Abstract
We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym [...] Read more.
We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kotera flow in the affine geometry, etc. Using the fact that two different curves in a given geometry are governed by the same integrable equation, we obtain Bäcklund transformations relating to these two integrable geometric flows. Some special solutions of the integrable systems are used to obtain the explicit Bäcklund transformations. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
Article
Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials
Symmetry 2015, 7(3), 1352-1375; https://doi.org/10.3390/sym7031352 - 03 Aug 2015
Cited by 39 | Viewed by 2708
Abstract
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 [...] Read more.
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schrödinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrödinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs. Full article
(This article belongs to the Special Issue Symmetry Breaking)
Review
A Framework for Symmetric Part Detection in Cluttered Scenes
Symmetry 2015, 7(3), 1333-1351; https://doi.org/10.3390/sym7031333 - 20 Jul 2015
Cited by 5 | Viewed by 3116
Abstract
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance [...] Read more.
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today’s recognition systems are faced with cluttered scenes and the assumption that a closed contour exists, i.e., that figure-ground segmentation has been solved, rendering much of the medial axis community’s work inapplicable. In this article, we review a computational framework, previously reported in [1–3], that bridges the representation power of the medial axis and the need to recover and group an object’s parts in a cluttered scene. Our framework is rooted in the idea that a maximally-inscribed disc, the building block of a medial axis, can be modelled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes. Full article
(This article belongs to the Special Issue Symmetry: Theory and Applications in Vision)
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Article
Computing with Colored Tangles
Symmetry 2015, 7(3), 1289-1332; https://doi.org/10.3390/sym7031289 - 20 Jul 2015
Cited by 5 | Viewed by 2441
Abstract
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated colored tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove [...] Read more.
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated colored tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete and with bounded resources that it can decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols. Full article
(This article belongs to the Special Issue Diagrams, Topology, Categories and Logic)
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Article
Development of Network Analysis and Visualization System for KEGG Pathways
Symmetry 2015, 7(3), 1275-1288; https://doi.org/10.3390/sym7031275 - 16 Jul 2015
Cited by 5 | Viewed by 3434
Abstract
Big data refers to informationalization technology for extracting valuable information through the use and analysis of large-scale data and, based on that data, deriving plans for response or predicting changes. With the development of software and devices for next generation sequencing, a vast [...] Read more.
Big data refers to informationalization technology for extracting valuable information through the use and analysis of large-scale data and, based on that data, deriving plans for response or predicting changes. With the development of software and devices for next generation sequencing, a vast amount of bioinformatics data has been generated recently. Also, bioinformatics data based big-data technology is rising rapidly as a core technology by the bioinformatician, biologist and big-data scientist. KEGG pathway is bioinformatics data for understanding high-level functions and utilities of the biological system. However, KEGG pathway analysis requires a lot of time and effort because KEGG pathways are high volume and very diverse. In this paper, we proposed a network analysis and visualization system that crawl user interest KEGG pathways, construct a pathway network based on a hierarchy structure of pathways and visualize relations and interactions of pathways by clustering and selecting core pathways from the network. Finally, we construct a pathway network collected by starting with an Alzheimer’s disease pathway and show the results on clustering and selecting core pathways from the pathway network. Full article
(This article belongs to the Special Issue Advanced Symmetry Modelling and Services in Future IT Environments)
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Obituary
In Memoriam: Slavik Jablan 1952–2015
Symmetry 2015, 7(3), 1261-1274; https://doi.org/10.3390/sym7031261 - 15 Jul 2015
Cited by 1 | Viewed by 2518
Abstract
After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...] Full article
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Article
The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric
Symmetry 2015, 7(3), 1211-1260; https://doi.org/10.3390/sym7031211 - 14 Jul 2015
Cited by 3 | Viewed by 5005
Abstract
The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for [...] Read more.
The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for the 64 codons of the codon set. (Hamming distances equal the number of different codon positions: AAA and AAC are at 1-distance; codons are maximally at 3-distance.) The CodonPolytope, a 9-dimensional geometric object, is spanned by 64 vertices that represent the codons and the Euclidian distances between these vertices correspond one-to-one with intercodon Hamming distances. The CodonGraph represents the vertices and edges of the polytope; each edge equals a Hamming 1-distance. The mirror reflection symmetry group of the polytope is isomorphic to the largest permutation symmetry group of the codon set that preserves Hamming distances. These groups contain 82,944 symmetries. Many polytope symmetries coincide with the degeneracy and similarity patterns of the genetic code. These code symmetries are strongly related with the face structure of the polytope with smaller faces displaying stronger code symmetries. Splitting the polytope stepwise into smaller faces models an early evolution of the code that generates this hierarchy of code symmetries. The canonical code represents a class of 41,472 codes with equivalent symmetries; a single class among an astronomical number of symmetry classes comprising all possible codes. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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Article
Real Time MODBUS Transmissions and Cryptography Security Designs and Enhancements of Protocol Sensitive Information
Symmetry 2015, 7(3), 1176-1210; https://doi.org/10.3390/sym7031176 - 02 Jul 2015
Cited by 63 | Viewed by 4081
Abstract
Information technology (IT) security has become a major concern due to the growing demand for information and massive development of client/server applications for various types of applications running on modern IT infrastructure. How has security been taken into account and which paradigms are [...] Read more.
Information technology (IT) security has become a major concern due to the growing demand for information and massive development of client/server applications for various types of applications running on modern IT infrastructure. How has security been taken into account and which paradigms are necessary to minimize security issues while increasing efficiency, reducing the influence on transmissions, ensuring protocol independency and achieving substantial performance? We have found cryptography to be an absolute security mechanism for client/server architectures, and in this study, a new security design was developed with the MODBUS protocol, which is considered to offer phenomenal performance for future development and enhancement of real IT infrastructure. This study is also considered to be a complete development because security is tested in almost all ways of MODBUS communication. The computed measurements are evaluated to validate the overall development, and the results indicate a substantial improvement in security that is differentiated from conventional methods. Full article
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Article
Hierarchical Clustering Using One-Class Support Vector Machines
Symmetry 2015, 7(3), 1164-1175; https://doi.org/10.3390/sym7031164 - 01 Jul 2015
Cited by 2 | Viewed by 2979
Abstract
This paper presents a novel hierarchical clustering method using support vector machines. A common approach for hierarchical clustering is to use distance for the task. However, different choices for computing inter-cluster distances often lead to fairly distinct clustering outcomes, causing interpretation difficulties in [...] Read more.
This paper presents a novel hierarchical clustering method using support vector machines. A common approach for hierarchical clustering is to use distance for the task. However, different choices for computing inter-cluster distances often lead to fairly distinct clustering outcomes, causing interpretation difficulties in practice. In this paper, we propose to use a one-class support vector machine (OC-SVM) to directly find high-density regions of data. Our algorithm generates nested set estimates using the OC-SVM and exploits the hierarchical structure of the estimated sets. We demonstrate the proposed algorithm on synthetic datasets. The cluster hierarchy is visualized with dendrograms and spanning trees. Full article
(This article belongs to the Special Issue Advanced Symmetry Modelling and Services in Future IT Environments)
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Article
Multiple Minimum Support-Based Rare Graph Pattern Mining Considering Symmetry Feature-Based Growth Technique and the Differing Importance of Graph Elements
Symmetry 2015, 7(3), 1151-1163; https://doi.org/10.3390/sym7031151 - 26 Jun 2015
Cited by 11 | Viewed by 2967
Abstract
Frequent graph pattern mining is one of the most interesting areas in data mining, and many researchers have developed a variety of approaches by suggesting efficient, useful mining techniques by integration of fundamental graph mining with other advanced mining works. However, previous graph [...] Read more.
Frequent graph pattern mining is one of the most interesting areas in data mining, and many researchers have developed a variety of approaches by suggesting efficient, useful mining techniques by integration of fundamental graph mining with other advanced mining works. However, previous graph mining approaches have faced fatal problems that cannot consider important characteristics in the real world because they cannot process both (1) different element importance and (2) multiple minimum support thresholds suitable for each graph element. In other words, graph elements in the real world have not only frequency factors but also their own importance; in addition, various elements composing graphs may require different thresholds according to their characteristics. However, traditional ones do not consider such features. To overcome these issues, we propose a new frequent graph pattern mining method, which can deal with both different element importance and multiple minimum support thresholds. Through the devised algorithm, we can obtain more meaningful graph pattern results with higher importance. We also demonstrate that the proposed algorithm has more outstanding performance compared to previous state-of-the-art approaches in terms of graph pattern generation, runtime, and memory usage. Full article
(This article belongs to the Special Issue Advanced Symmetry Modelling and Services in Future IT Environments)
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