Symmetry
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Latest open access articles published in Symmetry at http://www.mdpi.com/journal/symmetry<![CDATA[Symmetry, Vol. 8, Pages 38: On Solutions for Linear and Nonlinear Schrödinger Equations with Variable Coefficients: A Computational Approach]]>
http://www.mdpi.com/2073-8994/8/6/38
In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, dark- and Peregrine-type soliton solutions for NLS with variable coefficients. As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. Finally, we test numerical approximations for the inhomogeneous paraxial wave equation by the Crank-Nicolson scheme with analytical solutions found using Riccati systems. These solutions include oscillating laser beams and Laguerre and Gaussian beams.Symmetry2016-05-2886Article10.3390/sym8060038382073-89942016-05-28doi: 10.3390/sym8060038Gabriel AmadorKiara ColonNathalie LunaGerardo MercadoEnrique PereiraErwin Suazo<![CDATA[Symmetry, Vol. 8, Pages 40: A Methodology and Tool for Investigation of Artifacts Left by the BitTorrent Client]]>
http://www.mdpi.com/2073-8994/8/6/40
The BitTorrent client application is a popular utility for sharing large files over the Internet. Sometimes, this powerful utility is used to commit cybercrimes, like sharing of illegal material or illegal sharing of legal material. In order to help forensics investigators to fight against these cybercrimes, we carried out an investigation of the artifacts left by the BitTorrent client. We proposed a methodology to locate the artifacts that indicate the BitTorrent client activity performed. Additionally, we designed and implemented a tool that searches for the evidence left by the BitTorrent client application in a local computer running Windows. The tool looks for the four files holding the evidence. The files are as follows: *.torrent, dht.dat, resume.dat, and settings.dat. The tool decodes the files, extracts important information for the forensic investigator and converts it into XML format. The results are combined into a single result file.Symmetry2016-05-2686Article10.3390/sym8060040402073-89942016-05-26doi: 10.3390/sym8060040Algimantas VenčkauskasVacius JusasKęstutis PaulikasJevgenijus Toldinas<![CDATA[Symmetry, Vol. 8, Pages 39: A
PT
-Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling]]>
http://www.mdpi.com/2073-8994/8/6/39
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively.Symmetry2016-05-2686Article10.3390/sym8060039392073-89942016-05-26doi: 10.3390/sym8060039Jesús Cuevas-MaraverBoris MalomedPanayotis Kevrekidis<![CDATA[Symmetry, Vol. 8, Pages 37: Optional Frame Selection Algorithm for Adaptive Symmetric Service of Augmented Reality Big Data on Smart Devices]]>
http://www.mdpi.com/2073-8994/8/5/37
Following recent technological advances in diverse mobile devices, including smartphones, tablets and smartwatches, in-depth studies aimed at improving the quality of augmented reality (AR) are currently ongoing. Smartphones feature the essential elements of AR implementation, such as a camera, a processor and a display in a single device. As a result, additional hardware expansion for AR implementation has become unnecessary, popularizing AR technology at the user level. In the early stages, low-level AR technology was used mainly in limited fields, including simple road guides and marker-based recognition. Due to advances in AR technology, the range of usage has expanded as diverse technologies and purposes are combined. Users’ expectations of AR technology have also increased with this trend, and a high quality of service (QoS), with high-resolution, high-quality images, is now available. However, there are limitations in terms of processing speed and graphic treatment with smart devices, which, due to their small size, have inferior performance compared to the desktop environment when processing data for the implementation of high-resolution, high-quality images. This paper proposes an optional frame-selection algorithm (OFSA), which eliminates the unnecessary work involved with redundant frames during rendering for adaptive symmetric service of augmented reality big data on smart devices. Moreover, the memory read-write delay of the internally-operating OFSA, is minimized by adding an adaptive operation function. It is possible to provide adaptive common AR images at an improved frame rate in heterogeneous smart devices with different levels of performance.Symmetry2016-05-2385Article10.3390/sym8050037372073-89942016-05-23doi: 10.3390/sym8050037HwiRim ByunJong ParkYoung-Sik Jeong<![CDATA[Symmetry, Vol. 8, Pages 36: Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum]]>
http://www.mdpi.com/2073-8994/8/5/36
Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical behaviour of nonlinear coherent states for generalised classes of models corresponding to the generalised ladder operators. A comparative analysis among them indicates that the models with quadratic spectrum are more nonclassical than the others. Our central result is further underpinned by the comparison of the degree of nonclassicality of squeezed states of the corresponding models.Symmetry2016-05-1985Article10.3390/sym8050036362073-89942016-05-19doi: 10.3390/sym8050036Anaelle HertzSanjib DeyVéronique HussinHichem Eleuch<![CDATA[Symmetry, Vol. 8, Pages 35: Symmetry-Based Conflict Detection and Resolution Method towards Web3D-based Collaborative Design]]>
http://www.mdpi.com/2073-8994/8/5/35
In the process of web3D-based collaborative design, it is necessary to completely prevent operation conflicts among designers due to distributed environments and complex 3D models. Therefore, conflict detection and conflict resolution are of great significance to attain an acceptable result. In order to facilitate effective and smooth design work, a symmetry-based collaborative design framework is proposed using the X3D operation models. Combined considerations cover both models and operations, while different operation strategies are utilized for conflict resolution in web-based collaborative design. The strategy can achieve automatic operation, real-time conflict detection based on dynamically adjustable time, and conflict auto-detection and resolution with designers’ customization. A proof-of-concept system is developed for verification. The proposed resolution shows good performance, scalability and interactivity in a case study.Symmetry2016-05-1185Article10.3390/sym8050035352073-89942016-05-11doi: 10.3390/sym8050035Mingjiu YuHongming CaiXiaoming MaLihong Jiang<![CDATA[Symmetry, Vol. 8, Pages 33: Multivariate Krawtchouk Polynomials and Composition Birth and Death Processes]]>
http://www.mdpi.com/2073-8994/8/5/33
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur naturally as spectral orthogonal polynomials in a Karlin and McGregor spectral representation of transition functions in a composition birth and death process. In this Markov composition process in continuous time, there are N independent and identically distributed birth and death processes each with support 0 , 1 , … . The state space in the composition process is the number of processes in the different states 0 , 1 , … . Dealing with the spectral representation requires new extensions of the multivariate Krawtchouk polynomials to orthogonal polynomials on a multinomial distribution with a countable infinity of states.Symmetry2016-05-0985Article10.3390/sym8050033332073-89942016-05-09doi: 10.3390/sym8050033Robert Griffiths<![CDATA[Symmetry, Vol. 8, Pages 34: Ranking Features on Psychological Dynamics of Cooperative Team Work through Bayesian Networks]]>
http://www.mdpi.com/2073-8994/8/5/34
The aim of this study is to rank some features that characterize the psychological dynamics of cooperative team work in order to determine priorities for interventions and formation: leading positive feedback, cooperative manager and collaborative manager features. From a dataset of 20 cooperative sport teams (403 soccer players), the characteristics of the prototypical sports teams are studied using an average Bayesian network (BN) and two special types of BNs, the Bayesian classifiers: naive Bayes (NB) and tree augmented naive Bayes (TAN). BNs are selected as they are able to produce probability estimates rather than predictions. BN results show that the antecessors (the “top” features ranked) are the team members’ expectations and their attraction to the social aspects of the task. The main node is formed by the cooperative behaviors, the consequences ranked at the BN bottom (ratified by the TAN trees and the instantiations made), the roles assigned to the members and their survival inside the same team. These results should help managers to determine contents and priorities when they have to face team-building actions.Symmetry2016-05-0985Article10.3390/sym8050034342073-89942016-05-09doi: 10.3390/sym8050034Pilar Fuster-ParraAlex García-MasJaume CantallopsF. PonsetiYuhua Luo<![CDATA[Symmetry, Vol. 8, Pages 32: The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs]]>
http://www.mdpi.com/2073-8994/8/5/32
Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs) from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.Symmetry2016-05-0685Article10.3390/sym8050032322073-89942016-05-06doi: 10.3390/sym8050032Unil YunGangin LeeChul-Hong Kim<![CDATA[Symmetry, Vol. 8, Pages 31: On Consistent Nonparametric Statistical Tests of Symmetry Hypotheses]]>
http://www.mdpi.com/2073-8994/8/5/31
Being able to formally test for symmetry hypotheses is an important topic in many fields, including environmental and physical sciences. In this paper, one concentrates on a large family of nonparametric tests of symmetry based on Cramér–von Mises statistics computed from empirical distribution and characteristic functions. These tests possess the highly desirable property of being universally consistent in the sense that they detect any kind of departure from symmetry as the sample size becomes large. The asymptotic behaviour of these test statistics under symmetry is deduced from the theory of first-order degenerate V-statistics. The issue of computing valid p-values is tackled using the multiplier bootstrap method suitably adapted to V-statistics, yielding elegant, easy-to-compute and quick procedures for testing symmetry. A special focus is put on tests of univariate symmetry, bivariate exchangeability and reflected symmetry; a simulation study indicates the good sampling properties of these tests. Finally, a framework for testing general symmetry hypotheses is introduced.Symmetry2016-05-0685Article10.3390/sym8050031312073-89942016-05-06doi: 10.3390/sym8050031Jean-François Quessy<![CDATA[Symmetry, Vol. 8, Pages 30: Old Game, New Rules: Rethinking the Form of Physics]]>
http://www.mdpi.com/2073-8994/8/5/30
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wavefunction in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.Symmetry2016-05-0685Essay10.3390/sym8050030302073-89942016-05-06doi: 10.3390/sym8050030Christian Baumgarten<![CDATA[Symmetry, Vol. 8, Pages 29: The Reality of Casimir Friction]]>
http://www.mdpi.com/2073-8994/8/5/29
For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with observations, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here, we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics.Symmetry2016-04-2885Review10.3390/sym8050029292073-89942016-04-28doi: 10.3390/sym8050029Kimball MiltonJohan HøyeIver Brevik<![CDATA[Symmetry, Vol. 8, Pages 28: An Ultrasonic Lens Design Based on Prefractal Structures]]>
http://www.mdpi.com/2073-8994/8/4/28
The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. Thus, both a Fresnel ultrasonic lens and an arrangement of rigid rings based on Cantor prefractals are analyzed. Results show that the focusing capacity of the modified fractal lens is better than the Fresnel lens. This new lens is believed to have potential applications for ultrasonic imaging and medical ultrasound fields.Symmetry2016-04-2184Letter10.3390/sym8040028282073-89942016-04-21doi: 10.3390/sym8040028Sergio Castiñeira-IbáñezDaniel Tarrazó-SerranoConstanza RubioPilar CandelasAntonio Uris<![CDATA[Symmetry, Vol. 8, Pages 27: E-Polytopes in Picard Groups of Smooth Rational Surfaces]]>
http://www.mdpi.com/2073-8994/8/4/27
In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2 k 1 and 1 k 2 via E-type Weyl action.Symmetry2016-04-2084Article10.3390/sym8040027272073-89942016-04-20doi: 10.3390/sym8040027Jae-Hyouk LeeYongJoo Shin<![CDATA[Symmetry, Vol. 8, Pages 25: Spontaneous Breakdown of the Time Reversal Symmetry]]>
http://www.mdpi.com/2073-8994/8/4/25
The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit ϵ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.Symmetry2016-04-2084Article10.3390/sym8040025252073-89942016-04-20doi: 10.3390/sym8040025Janos Polonyi<![CDATA[Symmetry, Vol. 8, Pages 26: Chiral Symmetry and the Nucleon-Nucleon Interaction]]>
http://www.mdpi.com/2073-8994/8/4/26
We review how nuclear forces emerge from low-energy quantum chromodynamics (QCD) via chiral effective field theory (EFT). During the past two decades, this approach has evolved into a powerful tool to derive nuclear two- and many-body forces in a systematic and model-independent way. We then focus on the nucleon-nucleon (N N) interaction and show in detail how, governed by chiral symmetry, the long- and intermediate-range of the N N potential builds up order by order. We proceed up to sixth order in small momenta, where convergence is achieved. The final result allows for a full assessment of the validity of the chiral EFT approach to the N N interaction.Symmetry2016-04-2084Article10.3390/sym8040026262073-89942016-04-20doi: 10.3390/sym8040026Ruprecht Machleidt<![CDATA[Symmetry, Vol. 8, Pages 23: Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566]]>
http://www.mdpi.com/2073-8994/8/4/23
The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf–Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf–Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two of them should be replaced by their correct intermediate formulations, but which ultimately violate internal consistency constraints of the governing equation. It is concluded that the recently proposed symmetry analysis method for functional integro-differential equations should not be adopted when aiming at a consistent and complete approach.Symmetry2016-04-1884Commentary10.3390/sym8040023232073-89942016-04-18doi: 10.3390/sym8040023Michael FrewerGeorge Khujadze<![CDATA[Symmetry, Vol. 8, Pages 24: Reply to Frewer et al. Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566]]>
http://www.mdpi.com/2073-8994/8/4/24
We reply to the comment by Frewer and Khujadze regarding our contribution “Lie Symmetry Analysis of the Hopf Functional-Differential Equation” (Symmetry 2015, 7(3), 1536). The method developed by the present authors considered the Lie group analysis of the Hopf equations with functional derivatives in the equation, not the integro-differential equations in general. It was based on previous contributions (Oberlack and Wacławczyk, Arch. Mech. 2006, 58; Wacławczyk and Oberlack, J. Math. Phys. 2013, 54). In fact, three of the symmetries calculated in (Symmetry 2015, 7(3), 1536) break due to internal consistency constrains and conditions imposed on test functions, the same concerns the corresponding symmetries derived by Frewer and Khujadze and another, spurious symmetry, which was not discussed by Frewer and Khujadze. As a result, the same set of symmetries is obtained with both approaches.Symmetry2016-04-1684Reply10.3390/sym8040024242073-89942016-04-16doi: 10.3390/sym8040024Marta WacławczykDaniel JanochaMartin Oberlack<![CDATA[Symmetry, Vol. 8, Pages 22: Local Dynamics in an Infinite Harmonic Chain]]>
http://www.mdpi.com/2073-8994/8/4/22
By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of the generalized Langevin equation. Also studied are the ergodicity and chaos in a local dynamical variable.Symmetry2016-04-1584Article10.3390/sym8040022222073-89942016-04-15doi: 10.3390/sym8040022M. Lee<![CDATA[Symmetry, Vol. 8, Pages 21: Anomalous Mirror Symmetry Generated by Optical Illusion]]>
http://www.mdpi.com/2073-8994/8/4/21
This paper introduces a new concept of mirror symmetry, called “anomalous mirror symmetry”, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown.Symmetry2016-04-0884Article10.3390/sym8040021212073-89942016-04-08doi: 10.3390/sym8040021Kokichi Sugihara<![CDATA[Symmetry, Vol. 8, Pages 20: Resource Symmetric Dispatch Model for Internet of Things on Advanced Logistics]]>
http://www.mdpi.com/2073-8994/8/4/20
Business applications in advanced logistics service are highly concurrent. In this paper, we propose a resource symmetric dispatch model for the concurrent and cooperative tasks of the Internet of Things. In the model, the terminals receive and deliver commands, data, and information with mobile networks, wireless networks, and sensor networks. The data and information are classified and processed by the clustering servers in the cloud service platform. The cluster service, resource dispatch, and load balance are cooperative for management and monitoring of every application case during the logistics service lifecycle. In order to support the high performance of cloud service, resource symmetric dispatch algorithm among clustering servers and load balancing method among multi-cores in one server, including NIO (Non-blocking Input/Output) and RMI (Remote Method Invocation) are utilized to dispatch the cooperation of computation and service resources.Symmetry2016-04-0584Article10.3390/sym8040020202073-89942016-04-05doi: 10.3390/sym8040020Guofeng QinLisheng WangQiyan Li<![CDATA[Symmetry, Vol. 8, Pages 19: Casorati Inequalities for Submanifolds in a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Symmetric Metric Connection]]>
http://www.mdpi.com/2073-8994/8/4/19
By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.Symmetry2016-03-3184Article10.3390/sym8040019192073-89942016-03-31doi: 10.3390/sym8040019Pan ZhangLiang Zhang<![CDATA[Symmetry, Vol. 8, Pages 18: Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation]]>
http://www.mdpi.com/2073-8994/8/4/18
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. With such a perturbation, we can prove uniqueness of a solution to the discrete problem and stability of the discrete solution. The discretization considered is then known to converge to the viscosity solution but no rate of convergence was known.Symmetry2016-03-2484Article10.3390/sym8040018182073-89942016-03-24doi: 10.3390/sym8040018Gerard Awanou<![CDATA[Symmetry, Vol. 8, Pages 17: Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light]]>
http://www.mdpi.com/2073-8994/8/3/17
We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.Symmetry2016-03-1983Article10.3390/sym8030017172073-89942016-03-19doi: 10.3390/sym8030017Heung-Ryoul Noh<![CDATA[Symmetry, Vol. 8, Pages 16: Pseudospin Symmetry as a Bridge between Hadrons and Nuclei]]>
http://www.mdpi.com/2073-8994/8/3/16
Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from the insight that pseudospin symmetry has relativistic origins . We show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei. Since QCD sum rules predict that the sum of the scalar and vector potentials is small, we discuss the quark origins of pseudospin symmetry in nuclei and spin symmetry in hadrons.Symmetry2016-03-1883Article10.3390/sym8030016162073-89942016-03-18doi: 10.3390/sym8030016Joseph Ginocchio<![CDATA[Symmetry, Vol. 8, Pages 14: Status of X(1835) and pp¯ Interaction from Chiral Symmetry]]>
http://www.mdpi.com/2073-8994/8/3/14
After the observation of the strong near-threshold enhancement of proton-antiproton mass spectrum in
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/
&#x3C8;
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&#x3B3;
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decay, lots of theoretical investigations have been available such as new resonance, the final-state
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interaction (FSI),
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bound state (or baryonium), glueball, or other exotic (tetra-quark) states. Here, we provide a short review on the current status, especially on the pertinent discussions concerning its relation to
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interaction, for which the emphasis is put on the recently constructed chiral potential.Symmetry2016-03-1783Article10.3390/sym8030014142073-89942016-03-17doi: 10.3390/sym8030014Yong-Feng LiuXian-Wei Kang<![CDATA[Symmetry, Vol. 8, Pages 15: Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations]]>
http://www.mdpi.com/2073-8994/8/3/15
A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.Symmetry2016-03-1783Article10.3390/sym8030015152073-89942016-03-17doi: 10.3390/sym8030015Rutwig Campoamor-Stursberg<![CDATA[Symmetry, Vol. 8, Pages 12: Dual Pairs of Holomorphic Representations of Lie Groups from a Vector-Coherent-State Perspective]]>
http://www.mdpi.com/2073-8994/8/3/12
It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive pairs of holomorphic representations which are bi-orthogonal duals of each other with respect to a simple Bargmann inner product. It is then shown that the dual of a standard holomorphic representation has an integral expression for its inner product, with a Bargmann measure and a simply-defined kernel, which is not restricted to discrete-series representations. Dual pairs of holomorphic representations also provide practical ways to construct orthonormal bases for unitary irreps which bypass the need for evaluating the integral expressions for their inner products. This leads to practical algorithms for the application of holomorphic representations to model problems with dynamical symmetries in physics.Symmetry2016-03-1683Article10.3390/sym8030012122073-89942016-03-16doi: 10.3390/sym8030012David RoweJoe Repka<![CDATA[Symmetry, Vol. 8, Pages 13: Bézier Triangles with G2 Continuity across Boundaries]]>
http://www.mdpi.com/2073-8994/8/3/13
PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G0 continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and blend the corresponding Bézier triangles using a univariate blending function formulated in terms of barycentric coordinates. This produces G2 continuity across boundaries while preserving G1 continuity at vertices. The sharpness of the blends can be controlled locally by varying the extent of these blending regions. We demonstrate the effectiveness of our technique by showing several modeling examples.Symmetry2016-03-1583Article10.3390/sym8030013132073-89942016-03-15doi: 10.3390/sym8030013Chang-Ki LeeHae-Do HwangSeung-Hyun Yoon<![CDATA[Symmetry, Vol. 8, Pages 11: A Combinatorial Approach to Time Asymmetry]]>
http://www.mdpi.com/2073-8994/8/3/11
In this paper, simple models for the multiverse are analyzed. Each universe is viewed as a path in a graph, and by considering very general statistical assumptions, essentially originating from Boltzmann, we can make the set of all such paths into a finite probability space. We can then also attempt to compute the probabilities for different kinds of behavior and in particular under certain conditions argue that an asymmetric behavior of the entropy should be much more probable than a symmetric one. This offers an explanation for the asymmetry of time as a broken symmetry in the multiverse. The focus here is on simple models which can be analyzed using methods from combinatorics. Although the computational difficulties rapidly become enormous when the size of the model grows, this still gives hints about how a full-scale model should behave.Symmetry2016-03-1583Article10.3390/sym8030011112073-89942016-03-15doi: 10.3390/sym8030011Martin Tamm<![CDATA[Symmetry, Vol. 8, Pages 10: Polarity Formation in Molecular Crystals as a Symmetry Breaking Effect]]>
http://www.mdpi.com/2073-8994/8/3/10
The transition of molecular crystals into a polar state is modeled by a one-dimensional Ising Hamiltonian in multipole expansion and a suitable order parameter. Two symmetry breakings are necessary for the transition: the translational and the spin flip invariance—the former being broken by geometric constraints, the latter by the interaction of the first non-zero multipole with the next order multipole. Two different behaviors of the thermal average of the order parameter as a function of position are found. The free energy per lattice site converges to a finite value in the thermodynamic limit showing the consistency of the model in a macroscopic representation.Symmetry2016-03-1183Article10.3390/sym8030010102073-89942016-03-11doi: 10.3390/sym8030010Luigi CannavacciuoloJürg Hulliger<![CDATA[Symmetry, Vol. 8, Pages 9: Duality in Geometric Graphs: Vector Graphs, Kirchhoff Graphs and Maxwell Reciprocal Figures]]>
http://www.mdpi.com/2073-8994/8/3/9
We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented by Fehribach, which can be defined independent of any matrix relations. In particular, we present simple cases in which vector graphs are guaranteed to be Kirchhoff or non-Kirchhoff. Next, we review Maxwell’s method of drawing reciprocal figures as he presented in 1864, using modern mathematical language. We then demonstrate cases in which R2-vector graphs defined from Maxwell reciprocals are “dual” Kirchhoff graphs. Given an example in which Maxwell’s theories are not sufficient to define vector graphs, we begin to explore other methods of developing dual Kirchhoff graphs.Symmetry2016-02-2983Article10.3390/sym803000992073-89942016-02-29doi: 10.3390/sym8030009Tyler ReeseRandy PaffenrothJoseph Fehribach<![CDATA[Symmetry, Vol. 8, Pages 8: New Upper Bound and Lower Bound for Degree-Based Network Entropy]]>
http://www.mdpi.com/2073-8994/8/2/8
The degree-based network entropy which is inspired by Shannon’s entropy concept becomes the information-theoretic quantity for measuring the structural information of graphs and complex networks. In this paper, we study some properties of the degree-based network entropy. Firstly we develop a refinement of Jensen’s inequality. Next we present the new and more accurate upper bound and lower bound for the degree-based network entropy only using the order, the size, the maximum degree and minimum degree of a network. The bounds have desirable performance to restrict the entropy in different kinds of graphs. Finally, we show an application to structural complexity analysis of a computer network modeled by a connected graph.Symmetry2016-02-1982Article10.3390/sym802000882073-89942016-02-19doi: 10.3390/sym8020008Guoxiang LuBingqing LiLijia Wang<![CDATA[Symmetry, Vol. 8, Pages 7: On the Boundedness and Symmetry Properties of the Fractal Sets Generated from Alternated Complex Map]]>
http://www.mdpi.com/2073-8994/8/2/7
A complex map can give rise to two kinds of fractal sets: the Julia sets and the parameters sets (or the connectivity loci) which represent different connectivity properties of the corresponding Julia sets. In the significative results of (Int. J. Bifurc. Chaos, 2009, 19:2123–2129) and (Nonlinear. Dyn. 2013, 73:1155–1163), the authors presented the two kinds of fractal sets of a class of alternated complex map and left some visually observations to be proved about the boundedness and symmetry properties of these fractal sets. In this paper, we improve the previous results by giving the strictly mathematical proofs of the two properties. Some simulations that verify the theoretical proofs are also included.Symmetry2016-01-2682Article10.3390/sym802000772073-89942016-01-26doi: 10.3390/sym8020007Da WangShuTang Liu<![CDATA[Symmetry, Vol. 8, Pages 6: Acknowledgement to Reviewers of Symmetry in 2015]]>
http://www.mdpi.com/2073-8994/8/1/6
The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]Symmetry2016-01-2181Editorial10.3390/sym801000662073-89942016-01-21doi: 10.3390/sym8010006Symmetry Editorial Office<![CDATA[Symmetry, Vol. 8, Pages 5: Symmetry in Sphere-Based Assembly Configuration Spaces]]>
http://www.mdpi.com/2073-8994/8/1/5
Many remarkably robust, rapid and spontaneous self-assembly phenomena occurring in nature can be modeled geometrically, starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical, as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates that correspond to various types of macrostates can significantly increase efficiency and accuracy, i.e., reduce the notorious complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency, as well as accuracy vs. efficiency trade-offs in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres, with the following goals. (1) We give new, formal definitions of various concepts relevant to the sphere-based assembly setting that occur in previous work and, in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously-developed concepts include, for example: (i) assembly configuration spaces; (ii) stratification of assembly configuration space into configurational regions defined by active constraint graphs; (iii) paths through the configurational regions; and (iv) coarse assembly pathways. (2) We then demonstrate the new symmetry concepts to compute the sizes and numbers of orbits in two example settings appearing in previous work. (3) Finally, we give formal statements of a variety of open problems and challenges using the new conceptual definitions.Symmetry2016-01-2181Article10.3390/sym801000552073-89942016-01-21doi: 10.3390/sym8010005Meera SitharamAndrew VinceMenghan WangMiklós Bóna<![CDATA[Symmetry, Vol. 8, Pages 4: Synthesis of Chiral Cyclic Carbonates via Kinetic Resolution of Racemic Epoxides and Carbon Dioxide]]>
http://www.mdpi.com/2073-8994/8/1/4
The catalytic synthesis of cyclic carbonates using carbon dioxide as a C1-building block is a highly active area of research. Here, we review the catalytic production of enantiomerically enriched cyclic carbonates via kinetic resolution of racemic epoxides catalysed by metal-containing catalyst systems.Symmetry2016-01-1481Review10.3390/sym801000442073-89942016-01-14doi: 10.3390/sym8010004Xiao WuJosé Castro-OsmaMichael North<![CDATA[Symmetry, Vol. 8, Pages 3: Organocatalytic Asymmetric α-Chlorination of 1,3-Dicarbonyl Compounds Catalyzed by 2-Aminobenzimidazole Derivatives]]>
http://www.mdpi.com/2073-8994/8/1/3
Bifunctional chiral 2-aminobenzimidazole derivatives 1 and 2 catalyze the enantioselective stereodivergent α-chlorination of β-ketoesters and 1,3-diketone derivatives with up to 50% ee using N-chlorosuccinimide (NCS) or 2,3,4,4,5,6-hexachloro-2,5-cyclohexadien-1-one as electrophilic chlorine sources.Symmetry2016-01-1381Article10.3390/sym801000332073-89942016-01-13doi: 10.3390/sym8010003Daniel SánchezAlejandro BaezaDiego Alonso<![CDATA[Symmetry, Vol. 8, Pages 2: Natural Abundance Isotopic Chirality in the Reagents of the Soai Reaction]]>
http://www.mdpi.com/2073-8994/8/1/2
Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars–Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.Symmetry2016-01-0881Article10.3390/sym801000222073-89942016-01-08doi: 10.3390/sym8010002Béla BarabásRóbert KurdiGyula Pályi<![CDATA[Symmetry, Vol. 8, Pages 1: Structural Properties and Biological Prediction of ({[(1E)-3-(1H-Imidazol-1-yl)-1-phenylpropylidene] amino}oxy)(4-methylphenyl)methanone: An In Silico Approach]]>
http://www.mdpi.com/2073-8994/8/1/1
Bioactive molecules are playing essential role in the field of drug discovery and various pharmaceutical applications. Vibrational spectral investigations of the anti-Candida agent ({[(1E)-3-(1H-imidazol-1-yl)-1-phenylpropylidene]amino}oxy)(4-methylphenyl)methanone ((1E)-IPMM) have been recorded and analyzed to understand its structural geometry, inter- and intra-molecular interactions. The equilibrium geometry, harmonic vibrational wavenumber, natural bond orbital (NBO) and Frontier orbital energy analyses have been carried out with the help of density functional theory with B3LYP/6-311++G(d,p) level of theory. The detailed vibrational assignments for the title molecule were performed on the basis of potential energy distribution analysis in order to unambiguously predict its modes. The calculated wavenumbers had good agreement with the experimental values. NBO analysis has confirmed the intramolecular charge transfer interactions. The predicted docking binding energy gave insight into the possible biological activity of the title molecule.Symmetry2015-12-2881Article10.3390/sym801000112073-89942015-12-28doi: 10.3390/sym8010001Maha AlmutairiDevarasu ManimaranIssac JoeOla SalehMohamed Attia<![CDATA[Symmetry, Vol. 7, Pages 2206-2223: Petrie Duality and the Anstee–Robertson Graph]]>
http://www.mdpi.com/2073-8994/7/4/2206
We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 17, the other non-orientable of genus 52, which embed the 40-vertex cage of valency 6 and girth 5 discovered independently by Robertson and Anstee. We prove that this map (discovered by Evans) and its Petrie dual are the only regular embeddings of this graph, together with a similar result for a graph of order 40, valency 6 and girth 3 with the same automorphism group.Symmetry2015-12-2174Article10.3390/sym7042206220622232073-89942015-12-21doi: 10.3390/sym7042206Gareth JonesMatan Ziv-Av<![CDATA[Symmetry, Vol. 7, Pages 2195-2205: Estrada Index of Random Bipartite Graphs]]>
http://www.mdpi.com/2073-8994/7/4/2195
The Estrada index of a graph \(G\) of \(n\) vertices is defined by \(EE(G)=\sum_{i=1}^ne^{\lambda_i}\), where \(\lambda_1,\lambda_2,\cdots,\lambda_n\) are the eigenvalues of \(G\). In this paper, we give upper and lower bounds of \(EE(G)\) for almost all bipartite graphs by investigating the upper and lower bounds of the spectrum of random matrices. We also formulate an exact estimate of \(EE(G)\) for almost all balanced bipartite graphs.Symmetry2015-12-0774Article10.3390/sym7042195219522052073-89942015-12-07doi: 10.3390/sym7042195Yilun Shang<![CDATA[Symmetry, Vol. 7, Pages 2181-2194: When and Why Did Brains Break Symmetry?]]>
http://www.mdpi.com/2073-8994/7/4/2181
Asymmetry of brain function is known to be widespread amongst vertebrates, and it seems to have appeared very early in their evolution. In fact, recent evidence of functional asymmetry in invertebrates suggests that even small brains benefit from the allocation of different functions to the left and right sides. This paper discusses the differing functions of the left and right sides of the brain, including the roles of the left and right antennae of bees (several species) in both short- and long-term recall of olfactory memories and in social behaviour. It considers the likely advantages of functional asymmetry in small and large brains and whether functional asymmetry in vertebrates and invertebrates is analogous or homologous. Neural or cognitive capacity can be enhanced both by the evolution of a larger brain and by lateralization of brain function: a possible reason why both processes occur side-by-side is offered.Symmetry2015-12-0274Review10.3390/sym7042181218121942073-89942015-12-02doi: 10.3390/sym7042181Lesley RogersGiorgio Vallortigara<![CDATA[Symmetry, Vol. 7, Pages 2150-2180: Quaternifications and Extensions of Current Algebras on S3]]>
http://www.mdpi.com/2073-8994/7/4/2150
Let \(\mathbf{H}\) be the quaternion algebra. Let \(\mathfrak{g}\) be a complex Lie algebra and let \(U(\mathfrak{g})\) be the enveloping algebra of \(\mathfrak{g}\). The quaternification \(\mathfrak{g}^{\mathbf{H}}=\)\(\,(\,\mathbf{H}\otimes U(\mathfrak{g}),\,[\quad,\quad]_{\mathfrak{g}^{\mathbf{H}}}\,)\) of \(\mathfrak{g}\) is defined by the bracket \( \big[\,\mathbf{z}\otimes X\,,\,\mathbf{w}\otimes Y\,\big]_{\mathfrak{g}^{\mathbf{H}}}\,=\)\(\,(\mathbf{z}\cdot \mathbf{w})\otimes\,(XY)\,- \)\(\, (\mathbf{w}\cdot\mathbf{z})\otimes (YX)\,,\nonumber \) for \(\mathbf{z},\,\mathbf{w}\in \mathbf{H}\) and {the basis vectors \(X\) and \(Y\) of \(U(\mathfrak{g})\).} Let \(S^3\mathbf{H}\) be the ( non-commutative) algebra of \(\mathbf{H}\)-valued smooth mappings over \(S^3\) and let \(S^3\mathfrak{g}^{\mathbf{H}}=S^3\mathbf{H}\otimes U(\mathfrak{g})\). The Lie algebra structure on \(S^3\mathfrak{g}^{\mathbf{H}}\) is induced naturally from that of \(\mathfrak{g}^{\mathbf{H}}\). We introduce a 2-cocycle on \(S^3\mathfrak{g}^{\mathbf{H}}\) by the aid of a tangential vector field on \(S^3\subset \mathbf{C}^2\) and have the corresponding central extension \(S^3\mathfrak{g}^{\mathbf{H}} \oplus(\mathbf{C}a)\). As a subalgebra of \(S^3\mathbf{H}\) we have the algebra of Laurent polynomial spinors \(\mathbf{C}[\phi^{\pm}]\) spanned by a complete orthogonal system of eigen spinors \(\{\phi^{\pm(m,l,k)}\}_{m,l,k}\) of the tangential Dirac operator on \(S^3\). Then \(\mathbf{C}[\phi^{\pm}]\otimes U(\mathfrak{g})\) is a Lie subalgebra of \(S^3\mathfrak{g}^{\mathbf{H}}\). We have the central extension \(\widehat{\mathfrak{g}}(a)= (\,\mathbf{C}[\phi^{\pm}] \otimes U(\mathfrak{g}) \,) \oplus(\mathbf{C}a)\) as a Lie-subalgebra of \(S^3\mathfrak{g}^{\mathbf{H}} \oplus(\mathbf{C}a)\). Finally we have a Lie algebra \(\widehat{\mathfrak{g}}\) which is obtained by adding to \(\widehat{\mathfrak{g}}(a)\) a derivation \(d\) which acts on \(\widehat{\mathfrak{g}}(a)\) by the Euler vector field \(d_0\). That is the \(\mathbf{C}\)-vector space \(\widehat{\mathfrak{g}}=\left(\mathbf{C}[\phi^{\pm}]\otimes U(\mathfrak{g})\right)\oplus(\mathbf{C}a)\oplus (\mathbf{C}d)\) endowed with the bracket \( \bigl[\,\phi_1\otimes X_1+ \lambda_1 a + \mu_1d\,,\phi_2\otimes X_2 + \lambda_2 a + \mu_2d\,\,\bigr]_{\widehat{\mathfrak{g}}} \, =\)\( (\phi_1\phi_2)\otimes (X_1\,X_2) \, -\,(\phi_2\phi_1)\otimes (X_2X_1)+\mu_1d_0\phi_2\otimes X_2- \) \(\mu_2d_0\phi_1\otimes X_1 + \) \( (X_1\vert X_2)c(\phi_1,\phi_2)a\,. \) When \(\mathfrak{g}\) is a simple Lie algebra with its Cartan subalgebra \(\mathfrak{h}\) we shall investigate the weight space decomposition of \(\widehat{\mathfrak{g}}\) with respect to the subalgebra \(\widehat{\mathfrak{h}}= (\phi^{+(0,0,1)}\otimes \mathfrak{h} )\oplus(\mathbf{C}a) \oplus(\mathbf{C}d)\).Symmetry2015-11-2774Article10.3390/sym7042150215021802073-89942015-11-27doi: 10.3390/sym7042150Tosiaki KoriYuto Imai<![CDATA[Symmetry, Vol. 7, Pages 2134-2149: Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes]]>
http://www.mdpi.com/2073-8994/7/4/2134
We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed.Symmetry2015-11-1774Article10.3390/sym7042134213421492073-89942015-11-17doi: 10.3390/sym7042134David JouMichele SciaccaMaria Mongiovì<![CDATA[Symmetry, Vol. 7, Pages 2108-2133: Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions]]>
http://www.mdpi.com/2073-8994/7/4/2108
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal invariance has led to enormous progress in equilibrium phase transitions, especially in two dimensions. Non-equilibrium phase transitions can arise in much larger portions of the parameter space than equilibrium phase transitions. The state of the art of recent attempts to generalise conformal invariance to a new generic symmetry, taking into account the different scaling behaviour of space and time, will be reviewed. Particular attention will be given to the causality properties as they follow for co-variant n-point functions. These are important for the physical identification of n-point functions as responses or correlators.Symmetry2015-11-1374Review10.3390/sym7042108210821332073-89942015-11-13doi: 10.3390/sym7042108Malte Henkel<![CDATA[Symmetry, Vol. 7, Pages 2062-2107: Cytoskeletal Symmetry Breaking and Chirality: From Reconstituted Systems to Animal Development]]>
http://www.mdpi.com/2073-8994/7/4/2062
Animal development relies on repeated symmetry breaking, e.g., during axial specification, gastrulation, nervous system lateralization, lumen formation, or organ coiling. It is crucial that asymmetry increases during these processes, since this will generate higher morphological and functional specialization. On one hand, cue-dependent symmetry breaking is used during these processes which is the consequence of developmental signaling. On the other hand, cells isolated from developing animals also undergo symmetry breaking in the absence of signaling cues. These spontaneously arising asymmetries are not well understood. However, an ever growing body of evidence suggests that these asymmetries can originate from spontaneous symmetry breaking and self-organization of molecular assemblies into polarized entities on mesoscopic scales. Recent discoveries will be highlighted and it will be discussed how actomyosin and microtubule networks serve as common biomechanical systems with inherent abilities to drive spontaneous symmetry breaking.Symmetry2015-11-1174Review10.3390/sym7042062206221072073-89942015-11-11doi: 10.3390/sym7042062Christian Pohl<![CDATA[Symmetry, Vol. 7, Pages 2047-2061: Similarity and a Duality for Fullerenes]]>
http://www.mdpi.com/2073-8994/7/4/2047
Fullerenes are molecules of carbon that are modeled by trivalent plane graphs with only pentagonal and hexagonal faces. Scaling up a fullerene gives a notion of similarity, and fullerenes are partitioned into similarity classes. In this expository article, we illustrate how the values of two important fullerene parameters can be deduced for all fullerenes in a similarity class by computing the values of these parameters for just the three smallest representatives of that class. In addition, it turns out that there is a natural duality theory for similarity classes of fullerenes based on one of the most important fullerene construction techniques: leapfrog construction. The literature on fullerenes is very extensive, and since this is a general interest journal, we will summarize and illustrate the fundamental results that we will need to develop similarity and this duality.Symmetry2015-11-0674Article10.3390/sym7042047204720612073-89942015-11-06doi: 10.3390/sym7042047Jennifer EdmondJack Graver<![CDATA[Symmetry, Vol. 7, Pages 2038-2046: Is the Hawking Quasilocal Energy “Newtonian”?]]>
http://www.mdpi.com/2073-8994/7/4/2038
The Misner–Sharp–Hernandez mass defined in general relativity and in spherical symmetry has been recognized as having a Newtonian character in previous literature. In order to better understand this feature we relax spherical symmetry and we study the generalization of the Misner–Sharp–Hernandez mass to general spacetimes, i.e., the Hawking quasilocal mass. The latter is decomposed into a matter contribution and a contribution coming solely from the Weyl tensor. The Weyl tensor is then decomposed into an electric part (which has a Newtonian counterpart) and a magnetic one (which does not), which further splits the quasilocal mass into “Newtonian” and “non-Newtonian” parts. Only the electric (Newtonian) part contributes to the quasilocal mass.Symmetry2015-11-0574Article10.3390/sym7042038203820462073-89942015-11-05doi: 10.3390/sym7042038Valerio Faraoni<![CDATA[Symmetry, Vol. 7, Pages 2025-2037: Concise Review: Asymmetric Cell Divisions in Stem Cell Biology]]>
http://www.mdpi.com/2073-8994/7/4/2025
Somatic stem cells are rare cells with unique properties residing in many organs and tissues. They are undifferentiated cells responsible for tissue regeneration and homeostasis, and contain both the capacity to self-renew in order to maintain their stem cell potential and to differentiate towards tissue-specific, specialized cells. However, the knowledge about the mechanisms controlling somatic stem cell fate decisions remains sparse. One mechanism which has been described to control daughter cell fates in selected somatic stem cell systems is the process of asymmetric cell division (ACD). ACD is a tightly regulated and evolutionary conserved process allowing a single stem or progenitor cell to produce two differently specified daughter cells. In this concise review, we will summarize and discuss current concepts about the process of ACD as well as different ACD modes. Finally, we will recapitulate the current knowledge and our recent findings about ACD in human hematopoiesis.Symmetry2015-11-0574Review10.3390/sym7042025202520372073-89942015-11-05doi: 10.3390/sym7042025Florian MurkeSymone CastroBernd GiebelAndré Görgens<![CDATA[Symmetry, Vol. 7, Pages 2009-2024: A Monge–Ampere Equation with an Unusual Boundary Condition]]>
http://www.mdpi.com/2073-8994/7/4/2009
We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.Symmetry2015-11-0574Article10.3390/sym7042009200920242073-89942015-11-05doi: 10.3390/sym7042009Marc Sedjro<![CDATA[Symmetry, Vol. 7, Pages 1989-2008: Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs]]>
http://www.mdpi.com/2073-8994/7/4/1989
We construct, for any given \( \ell = \frac{1}{2} + {\mathbb N}_0, \) second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is observed that the invariant PDEs have significant difference for \( \ell &gt; \frac{1}{3}. \)Symmetry2015-11-0374Article10.3390/sym7041989198920082073-89942015-11-03doi: 10.3390/sym7041989Naruhiko AizawaTadanori Kato<![CDATA[Symmetry, Vol. 7, Pages 1981-1988: A Hypothesis for Self-Organization and Symmetry Reduction in the Synchronization of Organ-Level Contractions in the Human Uterus during Labor]]>
http://www.mdpi.com/2073-8994/7/4/1981
We present a hypothesis for a mechanism involving self-organization of small functional units that leads to organ-level synchronization of uterine contractions in human labor. This view is in contrast to the long-held presumption that the synchronized behavior of the uterus is subject to well-defined internal organization (as is found in the heart) that exists prior to the onset of labor. The contractile units of the uterus are myocytes, which contract in response to both mechanical stretch and electrical stimulation. Throughout pregnancy progesterone maintains quiescence by suppression of “contraction-associated proteins” (CAPs). At the end of pregnancy a functional withdrawal of progesterone and an increasingly estrogenic environment leads to an increase in the production of CAPs. One CAP of particular importance is connexin 43, which creates gap junctions between the myocytes that cause them to become electrically coupled. The electrical connectivity between myocytes, combined with an increase in intrauterine pressure at the end of pregnancy shifts the uterus towards an increasingly unstable critical point, characterized by irregular, uncoordinated contractions. We propose that synchronous, coordinated contractions emerge from this critical point through a process of self-organization, and that the search for a uterine pacemaker has been unfruitful for the sole reason that it is non-existent.Symmetry2015-10-2874Article10.3390/sym7041981198119882073-89942015-10-28doi: 10.3390/sym7041981David BanneyRoger YoungJonathan PaulMohammad ImtiazRoger Smith<![CDATA[Symmetry, Vol. 7, Pages 1945-1980: New Security Development and Trends to Secure the SCADA Sensors Automated Transmission during Critical Sessions]]>
http://www.mdpi.com/2073-8994/7/4/1945
Modern technology enhancements have been used worldwide to fulfill the requirements of the industrial sector, especially in supervisory control and data acquisition (SCADA) systems as a part of industrial control systems (ICS). SCADA systems have gained popularity in industrial automations due to technology enhancements and connectivity with modern computer networks and/or protocols. The procurement of new technologies has made SCADA systems important and helpful to processing in oil lines, water treatment plants, and electricity generation and control stations. On the other hand, these systems have vulnerabilities like other traditional computer networks (or systems), especially when interconnected with open platforms. Many international organizations and researchers have proposed and deployed solutions for SCADA security enhancement, but most of these have been based on node-to-node security, without emphasizing critical sessions that are linked directly with industrial processing and automation. This study concerns SCADA security measures related to critical processing with specified sessions of automated polling, analyzing cryptography mechanisms and deploying the appropriate explicit inclusive security solution in a distributed network protocol version 3 (DNP3) stack, as part of a SCADA system. The bytes flow through the DNP3 stack with security computational bytes within specified critical intervals defined for polling. We took critical processing knowledge into account when designing a SCADA/DNP3 testbed and deploying a cryptography solution that did not affect communications.Symmetry2015-10-2374Article10.3390/sym7041945194519802073-89942015-10-23doi: 10.3390/sym7041945Aamir ShahzadMalrey LeeHyung KimSeon-mi WooNaixue Xiong<![CDATA[Symmetry, Vol. 7, Pages 1929-1944: An Application of Equivalence Transformations to Reaction Diffusion Equations]]>
http://www.mdpi.com/2073-8994/7/4/1929
In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.Symmetry2015-10-2374Article10.3390/sym7041929192919442073-89942015-10-23doi: 10.3390/sym7041929Mariano TorrisiRita Tracinà<![CDATA[Symmetry, Vol. 7, Pages 1914-1928: Generation of Supramolecular Chirality around Twofold Rotational or Helical Axes in Crystalline Assemblies of Achiral Components]]>
http://www.mdpi.com/2073-8994/7/4/1914
A multi-point approximation method clarifies supramolecular chirality of twofold rotational or helical assemblies as well as bundles of the one-dimensional (1D) assemblies. While one-point approximation of materials claims no chirality generation of such assemblies, multi-point approximations do claim possible generation in the 1D assemblies of bars and plates. Such chirality derives from deformations toward three-axial directions around the helical axes. The chiral columns are bundled in chiral ways through symmetry operations. The preferable right- or left-handed columns are bundled together to yield chiral crystals with right- or left-handedness, respectively, indicating that twofold helix symmetry operations cause chiral crystals composed of achiral components via a three-stepwise and three-directional process.Symmetry2015-10-2174Review10.3390/sym7041914191419282073-89942015-10-21doi: 10.3390/sym7041914Mikiji MiyataNorimitsu TohnaiIchiro HisakiToshiyuki Sasaki<![CDATA[Symmetry, Vol. 7, Pages 1882-1913: Age Estimation-Based Soft Biometrics Considering Optical Blurring Based on Symmetrical Sub-Blocks for MLBP]]>
http://www.mdpi.com/2073-8994/7/4/1882
Because of its many useful applications, human age estimation has been considered in many previous studies as a soft biometrics. However, most existing methods of age estimation require a clear and focused facial image as input in order to obtain a trustworthy estimation result; otherwise, the methods might produce increased estimation error when an image of poor quality is used as input. Image blurring is one of major factors that affect estimation accuracies because it can cause a face to appear younger (i.e., reduce the age feature in the face region). Therefore, we propose a new human age estimation method that is robust even with an image that has the optical blurring effect by using symmetrical focus mask and sub-blocks for multi-level local binary pattern (MLBP). Experiment results show that the proposed method can enhance age estimation accuracy compared with the conventional system, which does not consider the effects of blurring.Symmetry2015-10-1974Article10.3390/sym7041882188219132073-89942015-10-19doi: 10.3390/sym7041882Dat NguyenSo ChoKang Park<![CDATA[Symmetry, Vol. 7, Pages 1856-1881: Anonymous Multi-Receiver Identity-Based Authenticated Encryption with CCA Security]]>
http://www.mdpi.com/2073-8994/7/4/1856
In a multi-receiver encryption system, a sender chooses a set of authorized receivers and sends them a message securely and efficiently, as the message is well encrypted and only one ciphertext corresponding to the message is generated no matter how many receivers the sender has chosen. It can be applied to video conferencing systems, pay-per-view channels, remote education, and so forth. Due to privacy considerations, an authorized receiver may not expect that his identity is revealed. In 2010, anonymous multi-receiver identity-based (ID-based) encryption was first discussed, and furthermore, many works on the topic have been presented so far. Unfortunately, we find that all of those schemes fail to prove the chosen ciphertext attacks (CCA) security in either confidentiality or anonymity. In this manuscript, we propose the first anonymous multi-receiver ID-based authenticated encryption scheme with CCA security in both confidentiality and anonymity. In the proposed scheme, the identity of the sender of a ciphertext can be authenticated by the receivers after a successful decryption. In addition, the proposed scheme also is the first CCA-secure one against insider attacks. Moreover, only one pairing computation is required in decryption.Symmetry2015-10-1674Article10.3390/sym7041856185618812073-89942015-10-16doi: 10.3390/sym7041856Chun-I FanYi-Fan Tseng<![CDATA[Symmetry, Vol. 7, Pages 1841-1855: Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems]]>
http://www.mdpi.com/2073-8994/7/4/1841
A wide range of reaction–diffusion systems with constant diffusivities that are invariant under Q-conditional operators is found. Using the symmetries obtained, the reductions of the corresponding systems to the systems of ODEs are conducted in order to find exact solutions. In particular, the solutions of some reaction–diffusion systems of the Lotka–Volterra type in an explicit form and satisfying Dirichlet boundary conditions are obtained. An biological interpretation is presented in order to show that two different types of interaction between biological species can be described.Symmetry2015-10-1674Article10.3390/sym7041841184118552073-89942015-10-16doi: 10.3390/sym7041841Oleksii Pliukhin<![CDATA[Symmetry, Vol. 7, Pages 1831-1840: On the Continuity of the Hutchinson Operator]]>
http://www.mdpi.com/2073-8994/7/4/1831
We investigate when the Hutchinson operator associated with an iterated function system is continuous. The continuity with respect to both the Hausdorff metric and Vietoris topology is carefully considered. An example showing that the Hutchinson operator on the hyperspace of nonempty closed bounded sets need not be Hausdorff continuous is given. Infinite systems are also discussed. The work clarifies and generalizes several partial results scattered across the literature.Symmetry2015-10-1574Article10.3390/sym7041831183118402073-89942015-10-15doi: 10.3390/sym7041831Michael BarnsleyKrzysztof Leśniak<![CDATA[Symmetry, Vol. 7, Pages 1816-1830: Lie Group Method for Solving the Generalized Burgers’, Burgers’–KdV and KdV Equations with Time-Dependent Variable Coefficients]]>
http://www.mdpi.com/2073-8994/7/4/1816
In this study, the Lie group method for constructing exact and numerical solutions of the generalized time-dependent variable coefficients Burgers’, Burgers’–KdV, and KdV equations with initial and boundary conditions is presented. Lie group theory is applied to determine symmetry reductions which reduce the nonlinear partial differential equations to ordinary differential equations. The obtained ordinary differential equations were solved analytically and the solutions are obtained in closed form for some specific choices of parameters, while others are solved numerically. In the obtained results we studied effects of both the time t and the index of nonlinearity on the behavior of the velocity, and the solutions are graphically presented.Symmetry2015-10-1374Article10.3390/sym7041816181618302073-89942015-10-13doi: 10.3390/sym7041816Mina Abd-el-MalekAmr Amin<![CDATA[Symmetry, Vol. 7, Pages 1803-1815: Classical and Quantum Burgers Fluids: A Challenge for Group Analysis]]>
http://www.mdpi.com/2073-8994/7/4/1803
The most general second order irrotational vector field evolution equation is constructed, that can be transformed to a single equation for the Cole–Hopf potential. The exact solution to the radial Burgers equation, with constant mass influx through a spherical supply surface, is constructed. The complex linear Schrödinger equation is equivalent to an integrable system of two coupled real vector equations of Burgers type. The first velocity field is the particle current divided by particle probability density. The second vector field gives a complex valued correction to the velocity that results in the correct quantum mechanical correction to the kinetic energy density of the Madelung fluid. It is proposed how to use symmetry analysis to systematically search for other constrained potential systems that generate a closed system of vector component evolution equations with constraints other than irrotationality.Symmetry2015-10-0974Article10.3390/sym7041803180318152073-89942015-10-09doi: 10.3390/sym7041803Philip Broadbridge<![CDATA[Symmetry, Vol. 7, Pages 1788-1802: Symbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine]]>
http://www.mdpi.com/2073-8994/7/4/1788
This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in traditional mechanical dynamic problems and current scientific disciplines. The conditions of being quasi-filiform and nilpotent are applied carefully and in several stages, and appropriate changes of the basis are achieved in an iterative and interactive process of simplification. This has been implemented by means of the development of more than thirty Maple modules. The process has led from the first family formulation, with 64 parameters and 215 constraints, to a family of 16 parameters and 17 constraints. This structure theorem permits the exhaustive classification of the quasi-filiform nilpotent Lie algebras of dimension nine with current computational methodologies.Symmetry2015-10-0174Article10.3390/sym7041788178818022073-89942015-10-01doi: 10.3390/sym7041788Mercedes PérezFrancisco PérezEmilio Jiménez<![CDATA[Symmetry, Vol. 7, Pages 1780-1787: Physics of the Chemical Asymmetry of the Cell Membrane: Implications in Gene Regulation and Pharmacology]]>
http://www.mdpi.com/2073-8994/7/4/1780
Signalling proteins are key regulators of basic cell physiology and tissues morphogenesis. Whilst signalling proteins are paramount for the cell to function optimally, their down regulation or inhibition is also central to tune the cell and its environment. One process involved in this tuning mechanism is membrane budding, otherwise known as endocytosis. The origin of the physical force driving the budding process and endocytosis has been the subject of much controversy. After two decades the budding process is now well described and it is acknowledged that fundamental principles from soft matter physics are at play. This opens a new window for understanding gene regulations, pharmacokinetic and multi drug resistance in cancer. This review recalls the first steps that have led to a better understanding of cell biology through the use of physics and; how the use of physics has shed light in areas of cell biology, cancer and pharmacology. It is, therefore, not a review of the many enzymes involved in membrane vesiculation and membrane curvature; it is more of an historical account.Symmetry2015-09-3074Review10.3390/sym7041780178017872073-89942015-09-30doi: 10.3390/sym7041780Ziad OmranPaula WilliamsCyril Rauch<![CDATA[Symmetry, Vol. 7, Pages 1768-1779: Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata]]>
http://www.mdpi.com/2073-8994/7/4/1768
To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA) models under regular and random initial conditions corresponds to three Wolfram’s classes of CAs, identified as Classes II, III, and IV. Regular initial conditions occur in two groups. One group that makes a broken, regular pattern formation has four types of symmetry, whereas the other group that makes a higher hierarchy pattern formation has only two types. Additionally, both final pattern formations show an increased amount of symmetropy as time passes. Moreover, the final pattern formations are affected by iterations of base rules of CA models of chaos dynamical systems. The growth design formations limit possibilities: the ratio of developing final pattern formations under a regular initial condition decreases in the order of Classes III, II, and IV. This might be related to the difference in degree in reference to surrounding conditions. These findings suggest that calculations of symmetries of the structures of one-dimensional cellular automata models are useful for revealing rules of pattern generation for animal bodies.Symmetry2015-09-2974Article10.3390/sym7041768176817792073-89942015-09-29doi: 10.3390/sym7041768Ikuko Tanaka<![CDATA[Symmetry, Vol. 7, Pages 1751-1767: New Nonlocal Symmetries of Diffusion-Convection Equations and Their Connection with Generalized Hodograph Transformation]]>
http://www.mdpi.com/2073-8994/7/4/1751
Additional nonlocal symmetries of diffusion-convection equations and the Burgers equation are obtained. It is shown that these equations are connected via a generalized hodograph transformation and appropriate nonlocal symmetries arise from additional Lie symmetries of intermediate equations. Two entirely different techniques are used to search nonlocal symmetry of a given equation: the first is based on usage of the characteristic equations generated by additional operators, another technique assumes the reconstruction of a parametrical Lie group transformation from such operator. Some of them are based on the nonlocal transformations that contain new independent variable determined by an auxiliary differential equation and allow the interpretation as a nonlocal transformation with additional variables. The formulae derived for construction of exact solutions are used.Symmetry2015-09-2974Article10.3390/sym7041751175117672073-89942015-09-29doi: 10.3390/sym7041751Valentyn Tychynin<![CDATA[Symmetry, Vol. 7, Pages 1734-1750: Fault Detection Based on Multi-Scale Local Binary Patterns Operator and Improved Teaching-Learning-Based Optimization Algorithm]]>
http://www.mdpi.com/2073-8994/7/4/1734
Aiming to effectively recognize train center plate bolt loss faults, this paper presents an improved fault detection method. A multi-scale local binary pattern operator containing the local texture information of different radii is designed to extract more efficient discrimination information. An improved teaching-learning-based optimization algorithm is established to optimize the classification results in the decision level. Two new phases including the worst recombination phase and the cuckoo search phase are incorporated to improve the diversity of the population and enhance the exploration. In the worst recombination phase, the worst solution is updated by a crossover recombination operation to prevent the premature convergence. The cuckoo search phase is adopted to escape the local optima. Experimental results indicate that the recognition accuracy is up to 98.9% which strongly demonstrates the effectiveness and reliability of the proposed detection method.Symmetry2015-09-2874Article10.3390/sym7041734173417502073-89942015-09-28doi: 10.3390/sym7041734Hongjian ZhangPing HeXudong Yang<![CDATA[Symmetry, Vol. 7, Pages 1721-1733: Symmetry Breaking and Establishment of Dorsal/Ventral Polarity in the Early Sea Urchin Embryo]]>
http://www.mdpi.com/2073-8994/7/4/1721
The mechanisms imposing the Dorsal/Ventral (DV) polarity of the early sea urchin embryo consist of a combination of inherited maternal information and inductive interactions among blastomeres. Old and recent studies suggest that a key molecular landmark of DV polarization is the expression of nodal on the future ventral side, in apparent contrast with other metazoan embryos, where nodal is expressed dorsally. A subtle maternally-inherited redox anisotropy, plus some maternal factors such as SoxB1, Univin, and p38-MAPK have been identified as inputs driving the spatially asymmetric transcription of nodal. However, all the mentioned factors are broadly distributed in the embryo as early as nodal transcription occurs, suggesting that repression of the gene in non-ventral territories depends upon negative regulators. Among these, the Hbox12 homeodomain-containing repressor is expressed by prospective dorsal cells, where it acts as a dorsal-specific negative modulator of the p38-MAPK activity. This review provides an overview of the molecular mechanisms governing the establishment of DV polarity in sea urchins, focusing on events taking place in the early embryo. Altogether, these findings provide a framework for future studies aimed to unravel the inceptive mechanisms involved in the DV symmetry breaking.Symmetry2015-09-2874Review10.3390/sym7041721172117332073-89942015-09-28doi: 10.3390/sym7041721Vincenzo CavalieriGiovanni Spinelli<![CDATA[Symmetry, Vol. 7, Pages 1699-1720: Cyclodextrins in Asymmetric and Stereospecific Synthesis]]>
http://www.mdpi.com/2073-8994/7/4/1699
Since their discovery, cyclodextrins have widely been used as green and easily available alternatives to promoters or catalysts of different chemical reactions in water. This review covers the research and application of cyclodextrins and their derivatives in asymmetric and stereospecific syntheses, with their division into three main groups: (1) cyclodextrins promoting asymmetric and stereospecific catalysis in water; (2) cyclodextrins’ complexes with transition metals as asymmetric and stereospecific catalysts; and (3) cyclodextrins’ non-metallic derivatives as asymmetric and stereospecific catalysts. The scope of this review is to systematize existing information on the contribution of cyclodextrins to asymmetric and stereospecific synthesis and, thus, to facilitate further development in this direction.Symmetry2015-09-2474Review10.3390/sym7041699169917202073-89942015-09-24doi: 10.3390/sym7041699Fliur MacaevVeaceslav Boldescu<![CDATA[Symmetry, Vol. 7, Pages 1670-1698: Application of Assistive Computer Vision Methods to Oyama Karate Techniques Recognition]]>
http://www.mdpi.com/2073-8994/7/4/1670
In this paper we propose a novel algorithm that enables online actions segmentation and classification. The algorithm enables segmentation from an incoming motion capture (MoCap) data stream, sport (or karate) movement sequences that are later processed by classification algorithm. The segmentation is based on Gesture Description Language classifier that is trained with an unsupervised learning algorithm. The classification is performed by continuous density forward-only hidden Markov models (HMM) classifier. Our methodology was evaluated on a unique dataset consisting of MoCap recordings of six Oyama karate martial artists including multiple champion of Kumite Knockdown Oyama karate. The dataset consists of 10 classes of actions and included dynamic actions of stands, kicks and blocking techniques. Total number of samples was 1236. We have examined several HMM classifiers with various number of hidden states and also Gaussian mixture model (GMM) classifier to empirically find the best setup of the proposed method in our dataset. We have used leave-one-out cross validation. The recognition rate of our methodology differs between karate techniques and is in the range of 81% ± 15% even to 100%. Our method is not limited for this class of actions but can be easily adapted to any other MoCap-based actions. The description of our approach and its evaluation are the main contributions of this paper. The results presented in this paper are effects of pioneering research on online karate action classification.Symmetry2015-09-2474Article10.3390/sym7041670167016982073-89942015-09-24doi: 10.3390/sym7041670Tomasz HachajMarek OgielaKatarzyna Koptyra<![CDATA[Symmetry, Vol. 7, Pages 1655-1669: An Elementary Derivation of the Matrix Elements of Real Irreducible Representations of so(3)]]>
http://www.mdpi.com/2073-8994/7/3/1655
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.Symmetry2015-09-1473Article10.3390/sym7031655165516692073-89942015-09-14doi: 10.3390/sym7031655Rutwig Campoamor-Stursberg<![CDATA[Symmetry, Vol. 7, Pages 1646-1654: Uncertainty Analysis of 208Pb Neutron Skin Predictions with Chiral Interactions]]>
http://www.mdpi.com/2073-8994/7/3/1646
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.Symmetry2015-09-1473Article10.3390/sym7031646164616542073-89942015-09-14doi: 10.3390/sym7031646Francesca Sammarruca<![CDATA[Symmetry, Vol. 7, Pages 1633-1645: Mirror Symmetry and Polar Duality of Polytopes]]>
http://www.mdpi.com/2073-8994/7/3/1633
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.Symmetry2015-09-1073Article10.3390/sym7031633163316452073-89942015-09-10doi: 10.3390/sym7031633David Cox<![CDATA[Symmetry, Vol. 7, Pages 1613-1632: Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model]]>
http://www.mdpi.com/2073-8994/7/3/1613
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.Symmetry2015-09-0873Article10.3390/sym7031613161316322073-89942015-09-08doi: 10.3390/sym7031613M.C. NucciG. Sanchini<![CDATA[Symmetry, Vol. 7, Pages 1595-1612: From Conformal Invariance towards Dynamical Symmetries of the Collisionless Boltzmann Equation]]>
http://www.mdpi.com/2073-8994/7/3/1595
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.Symmetry2015-09-0773Article10.3390/sym7031595159516122073-89942015-09-07doi: 10.3390/sym7031595Stoimen StoimenovMalte Henkel<![CDATA[Symmetry, Vol. 7, Pages 1587-1594: Prevention of Exponential Equivalence in Simple Password Exponential Key Exchange (SPEKE)]]>
http://www.mdpi.com/2073-8994/7/3/1587
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.Symmetry2015-09-0273Article10.3390/sym7031587158715942073-89942015-09-02doi: 10.3390/sym7031587Hanwook LeeDongho Won<![CDATA[Symmetry, Vol. 7, Pages 1567-1586: Design of IP Camera Access Control Protocol by Utilizing Hierarchical Group Key]]>
http://www.mdpi.com/2073-8994/7/3/1567
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.Symmetry2015-08-2773Article10.3390/sym7031567156715862073-89942015-08-27doi: 10.3390/sym7031567Jungho KangJaekyung HanJong Park<![CDATA[Symmetry, Vol. 7, Pages 1536-1566: Lie Symmetry Analysis of the Hopf Functional-Differential Equation]]>
http://www.mdpi.com/2073-8994/7/3/1536
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.Symmetry2015-08-2773Article10.3390/sym7031536153615662073-89942015-08-27doi: 10.3390/sym7031536Daniel JanochaMarta WacławczykMartin Oberlack<![CDATA[Symmetry, Vol. 7, Pages 1519-1535: Enantioselective Organocatalyzed Synthesis of 2-Amino-3-cyano-4H-chromene Derivatives]]>
http://www.mdpi.com/2073-8994/7/3/1519
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.Symmetry2015-08-2673Review10.3390/sym7031519151915352073-89942015-08-26doi: 10.3390/sym7031519Isaac SonsonaEugenia Marqués-LópezRaquel Herrera<![CDATA[Symmetry, Vol. 7, Pages 1475-1518: Performance Enhancement of Face Recognition in Smart TV Using Symmetrical Fuzzy-Based Quality Assessment]]>
http://www.mdpi.com/2073-8994/7/3/1475
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.Symmetry2015-08-2573Article10.3390/sym7031475147515182073-89942015-08-25doi: 10.3390/sym7031475Yeong Kim Won LeeKi KimHyung HongKang Park<![CDATA[Symmetry, Vol. 7, Pages 1463-1474: A (1+2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions]]>
http://www.mdpi.com/2073-8994/7/3/1463
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.Symmetry2015-08-2473Article10.3390/sym7031463146314742073-89942015-08-24doi: 10.3390/sym7031463Maksym Didovych<![CDATA[Symmetry, Vol. 7, Pages 1455-1462: Estrada and L-Estrada Indices of Edge-Independent Random Graphs]]>
http://www.mdpi.com/2073-8994/7/3/1455
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.Symmetry2015-08-1973Technical Note10.3390/sym7031455145514622073-89942015-08-19doi: 10.3390/sym7031455Yilun Shang<![CDATA[Symmetry, Vol. 7, Pages 1436-1454: Asymmetry Assessment Using Surface Topography in Healthy Adolescents]]>
http://www.mdpi.com/2073-8994/7/3/1436
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.Symmetry2015-08-1773Article10.3390/sym7031436143614542073-89942015-08-17doi: 10.3390/sym7031436Connie HoEric ParentElise WatkinsMarc MoreauDouglas HeddenMarwan El-RichSamer Adeeb<![CDATA[Symmetry, Vol. 7, Pages 1410-1435: Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2)-Dimensional Boundary Value Problems]]>
http://www.mdpi.com/2073-8994/7/3/1410
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.Symmetry2015-08-1773Article10.3390/sym7031410141014352073-89942015-08-17doi: 10.3390/sym7031410Roman ChernihaJohn King<![CDATA[Symmetry, Vol. 7, Pages 1395-1409: Enantioselective Organocatalysis in Microreactors: Continuous Flow Synthesis of a (S)-Pregabalin Precursor and (S)-Warfarin]]>
http://www.mdpi.com/2073-8994/7/3/1395
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.Symmetry2015-08-0473Article10.3390/sym7031395139514092073-89942015-08-04doi: 10.3390/sym7031395Riccardo PortaMaurizio BenagliaFrancesca CocciaSergio RossiAlessandra Puglisi<![CDATA[Symmetry, Vol. 7, Pages 1376-1394: Bäcklund Transformations for Integrable Geometric Curve Flows]]>
http://www.mdpi.com/2073-8994/7/3/1376
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.Symmetry2015-08-0373Article10.3390/sym7031376137613942073-89942015-08-03doi: 10.3390/sym7031376Changzheng QuJingwei HanJing Kang<![CDATA[Symmetry, Vol. 7, Pages 1352-1375: Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials]]>
http://www.mdpi.com/2073-8994/7/3/1352
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.Symmetry2015-08-0373Article10.3390/sym7031352135213752073-89942015-08-03doi: 10.3390/sym7031352Ratbay MyrzakulovGalya MamyrbekovaGulgassyl NugmanovaMuthusamy Lakshmanan<![CDATA[Symmetry, Vol. 7, Pages 1333-1351: A Framework for Symmetric Part Detection in Cluttered Scenes]]>
http://www.mdpi.com/2073-8994/7/3/1333
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.Symmetry2015-07-2073Review10.3390/sym7031333133313512073-89942015-07-20doi: 10.3390/sym7031333Tom LeeSanja FidlerAlex LevinshteinCristian SminchisescuSven Dickinson<![CDATA[Symmetry, Vol. 7, Pages 1289-1332: Computing with Colored Tangles]]>
http://www.mdpi.com/2073-8994/7/3/1289
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.Symmetry2015-07-2073Article10.3390/sym7031289128913322073-89942015-07-20doi: 10.3390/sym7031289Avishy CarmiDaniel Moskovich<![CDATA[Symmetry, Vol. 7, Pages 1275-1288: Development of Network Analysis and Visualization System for KEGG Pathways]]>
http://www.mdpi.com/2073-8994/7/3/1275
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.Symmetry2015-07-1673Article10.3390/sym7031275127512882073-89942015-07-16doi: 10.3390/sym7031275Dongmin SeoMin-Ho LeeSeok Yu<![CDATA[Symmetry, Vol. 7, Pages 1261-1274: In Memoriam: Slavik Jablan 1952–2015]]>
http://www.mdpi.com/2073-8994/7/3/1261
After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...]Symmetry2015-07-1573Obituary10.3390/sym7031261126112742073-89942015-07-15doi: 10.3390/sym7031261Donald CroweGyörgy DarvasDirk HuylebrouckJay KappraffLouis KauffmanSofia LambropoulouJozef PrzytyckiLjiljana RadovićRadmila SazdanovicVera de SpinadelAna ZekovićSymmetry Office<![CDATA[Symmetry, Vol. 7, Pages 1211-1260: The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric]]>
http://www.mdpi.com/2073-8994/7/3/1211
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.Symmetry2015-07-1473Article10.3390/sym7031211121112602073-89942015-07-14doi: 10.3390/sym7031211Reijer Lenstra<![CDATA[Symmetry, Vol. 7, Pages 1176-1210: Real Time MODBUS Transmissions and Cryptography Security Designs and Enhancements of Protocol Sensitive Information]]>
http://www.mdpi.com/2073-8994/7/3/1176
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.Symmetry2015-07-0273Article10.3390/sym7031176117612102073-89942015-07-02doi: 10.3390/sym7031176Aamir ShahzadMalrey LeeYoung-Keun LeeSuntae KimNaixue XiongJae-Young ChoiYounghwa Cho<![CDATA[Symmetry, Vol. 7, Pages 1164-1175: Hierarchical Clustering Using One-Class Support Vector Machines]]>
http://www.mdpi.com/2073-8994/7/3/1164
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.Symmetry2015-07-0173Article10.3390/sym7031164116411752073-89942015-07-01doi: 10.3390/sym7031164Gyemin Lee<![CDATA[Symmetry, Vol. 7, Pages 1151-1163: Multiple Minimum Support-Based Rare Graph Pattern Mining Considering Symmetry Feature-Based Growth Technique and the Differing Importance of Graph Elements]]>
http://www.mdpi.com/2073-8994/7/3/1151
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.Symmetry2015-06-2673Article10.3390/sym7031151115111632073-89942015-06-26doi: 10.3390/sym7031151Gangin LeeUnil YunHeungmo RyangDonggyu Kim<![CDATA[Symmetry, Vol. 7, Pages 1122-1150: Symmetry-Breaking as a Paradigm to Design Highly-Sensitive Sensor Systems]]>
http://www.mdpi.com/2073-8994/7/2/1122
A large class of dynamic sensors have nonlinear input-output characteristics, often corresponding to a bistable potential energy function that controls the evolution of the sensor dynamics. These sensors include magnetic field sensors, e.g., the simple fluxgate magnetometer and the superconducting quantum interference device (SQUID), ferroelectric sensors and mechanical sensors, e.g., acoustic transducers, made with piezoelectric materials. Recently, the possibilities offered by new technologies and materials in realizing miniaturized devices with improved performance have led to renewed interest in a new generation of inexpensive, compact and low-power fluxgate magnetometers and electric-field sensors. In this article, we review the analysis of an alternative approach: a symmetry-based design for highly-sensitive sensor systems. The design incorporates a network architecture that produces collective oscillations induced by the coupling topology, i.e., which sensors are coupled to each other. Under certain symmetry groups, the oscillations in the network emerge via an infinite-period bifurcation, so that at birth, they exhibit a very large period of oscillation. This characteristic renders the oscillatory wave highly sensitive to symmetry-breaking effects, thus leading to a new detection mechanism. Model equations and bifurcation analysis are discussed in great detail. Results from experimental works on networks of fluxgate magnetometers are also included.Symmetry2015-06-1972Review10.3390/sym7021122112211502073-89942015-06-19doi: 10.3390/sym7021122Antonio PalaciosVisarath InPatrick Longhini<![CDATA[Symmetry, Vol. 7, Pages 1080-1121: An Extended Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets]]>
http://www.mdpi.com/2073-8994/7/2/1080
This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges and internal symmetries provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.Symmetry2015-06-1672Article10.3390/sym7021080108011212073-89942015-06-16doi: 10.3390/sym7021080Sylvester GatesJames ParkerVincent RodgersLeo RodriguezKory Stiffler<![CDATA[Symmetry, Vol. 7, Pages 1061-1079: Symmetry Extraction in High Sensitivity Melanoma Diagnosis]]>
http://www.mdpi.com/2073-8994/7/2/1061
Melanoma diagnosis depends on the experience of doctors. Symmetry is one of the most important factors to measure, since asymmetry shows an uncontrolled growth of cells, leading to melanoma cancer. A system for melanoma detection in diagnosing melanocytic diseases with high sensitivity is proposed here. Two different sets of features are extracted based on the importance of the ABCD rule and symmetry evaluation to develop a new architecture. Support Vector Machines are used to classify the extracted sets by using both an alternative labeling method and a structure divided into two different classifiers which prioritize sensitivity. Although feature extraction is based on former works, the novelty lies in the importance given to symmetry and the proposed architecture, which combines two different feature sets to obtain a high sensitivity, prioritizing the medical aspect of diagnosis. In particular, a database provided by Hospital Universitario de Gran Canaria Doctor Negrín was tested, obtaining a sensitivity of 100% and a specificity of 66.66% using a leave-one-out validation method. These results show that 66.66% of biopsies would be avoided if this system is applied to lesions which are difficult to classify by doctors.Symmetry2015-06-1572Article10.3390/sym7021061106110792073-89942015-06-15doi: 10.3390/sym7021061Elyoenai Guerra-SeguraCarlos Travieso-GonzálezJesús Alonso-HernándezAntonio Ravelo-GarcíaGregorio Carretero<![CDATA[Symmetry, Vol. 7, Pages 1043-1060: Kinematic Skeleton Based Control of a Virtual Simulator for Military Training]]>
http://www.mdpi.com/2073-8994/7/2/1043
Virtual simulation technology has been considered as a highly efficient and cost-effective solution for a soldier training system, and evolved into diverse combinations of hardware and software. To maximize the virtual reality effect within a restricted space, a locomotion interface such as an omni-directional treadmill is introduced as a major component of a virtual simulator, therefore real time interaction between human and the virtual simulator becomes very important. Displacement and heading changes of the trainee are crucial information to control the virtual simulator when we implement highly reactive motion control for the omni-directional treadmill and interaction control of the virtual contents. This paper proposes a control parameter estimation algorithm for the virtual training simulator by using two types of motion capture sensors and presents the experimental results. Kinematic joint positions are analyzed to estimate the trainee’s location and velocity for feedback and feedforward control of the omni-directional treadmill. The accuracy of two approaches is evaluated by comparing with the reference system, which gives a ground truth value.Symmetry2015-06-1172Article10.3390/sym7021043104310602073-89942015-06-11doi: 10.3390/sym7021043Soyeon LeeSangjoon ParkKyoil ChungChoongho Cho<![CDATA[Symmetry, Vol. 7, Pages 1040-1042: Symmetry Best Paper Award 2015]]>
http://www.mdpi.com/2073-8994/7/2/1040
In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015:Symmetry2015-06-0872Editorial10.3390/sym7021040104010422073-89942015-06-08doi: 10.3390/sym7021040Sergei Odintsov