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Symmetry, Volume 6, Issue 2 (June 2014), Pages 164-472

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Research

Jump to: Review, Other

Open AccessArticle Spacetime Metrics from Gauge Potentials
Symmetry 2014, 6(2), 164-170; doi:10.3390/sym6020164
Received: 27 January 2014 / Revised: 21 March 2014 / Accepted: 24 March 2014 / Published: 27 March 2014
PDF Full-text (198 KB) | HTML Full-text | XML Full-text
Abstract
I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the
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I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S3 cosmological metric. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
Open AccessArticle Development of Symmetry Concepts for Aperiodic Crystals
Symmetry 2014, 6(2), 171-188; doi:10.3390/sym6020171
Received: 21 February 2014 / Revised: 18 March 2014 / Accepted: 26 March 2014 / Published: 31 March 2014
Cited by 1 | PDF Full-text (493 KB) | HTML Full-text | XML Full-text
Abstract
An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank.
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An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. Further extensions use time reversal and time translation operations on magnetic and electrodynamic systems. An alternative description of magnetic structures to that with symmetry groups, the Shubnikov groups, is using representations of space groups. The same can be done for aperiodic crystals. A discussion of the relation between the two approaches is given. Representations of space groups and superspace groups play a role in the study of physical properties. These, and generalizations of them, are discussed for aperiodic crystals. They are used, in particular, for the characterization of phase transitions between aperiodic crystal phases. Full article
(This article belongs to the Special Issue Crystal Symmetry and Structure)
Open AccessArticle Topological Symmetry Groups of Small Complete Graphs
Symmetry 2014, 6(2), 189-209; doi:10.3390/sym6020189
Received: 12 February 2014 / Revised: 2 April 2014 / Accepted: 2 April 2014 / Published: 8 April 2014
Cited by 2 | PDF Full-text (266 KB) | HTML Full-text | XML Full-text
Abstract
Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R3. In this paper, we determine for each complete graph Kn with n
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Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R3. In this paper, we determine for each complete graph Kn with n ≤ 6, what groups can occur as topological symmetry groups or orientation preserving topological symmetry groups of some embedding of the graph in R3. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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Open AccessArticle Domain Specificity in Human Symmetry Preferences: Symmetry is Most Pleasant When Looking at Human Faces
Symmetry 2014, 6(2), 222-233; doi:10.3390/sym6020222
Received: 21 February 2014 / Revised: 24 March 2014 / Accepted: 26 March 2014 / Published: 17 April 2014
Cited by 2 | PDF Full-text (3443 KB) | HTML Full-text | XML Full-text
Abstract
Visual symmetry has been found to be preferred to asymmetry in a variety of domains and across species. A number of theories propose to explain why symmetry is preferred. In this article, I compare a perceptual bias view, in which symmetry is preferred
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Visual symmetry has been found to be preferred to asymmetry in a variety of domains and across species. A number of theories propose to explain why symmetry is preferred. In this article, I compare a perceptual bias view, in which symmetry is preferred due to factors inherit to the visual system, and an evolutionary advantage view, in which symmetry is preferred due to selection pressures on partner preference. Preferences for symmetry in three stimulus types were determined by having symmetric and asymmetric versions of the same images rated for pleasantness: human female faces, macaque monkey faces, and abstract art. It was found that preferences for symmetry were strongest for human female faces and weakest for art. This finding builds on previous research suggesting that symmetry preferences for human faces are different from symmetry preferences in other domains and that simple perceptual bias explanations do not wholly explain human visual face symmetry preferences. While consistent with an evolutionary advantage view, these data are also potentially explainable via a perceptual bias view which accounts for experience of stimuli. The interplay between these two views is discussed in the context of the current study. Full article
(This article belongs to the Special Issue Visual Symmetry)
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Open AccessArticle Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Symmetry 2014, 6(2), 295-307; doi:10.3390/sym6020295
Received: 27 February 2014 / Revised: 14 April 2014 / Accepted: 18 April 2014 / Published: 23 April 2014
Cited by 3 | PDF Full-text (179 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in
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In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
Open AccessArticle The Almost Periodic Rigidity of Crystallographic Bar-Joint Frameworks
Symmetry 2014, 6(2), 308-328; doi:10.3390/sym6020308
Received: 25 February 2014 / Revised: 11 April 2014 / Accepted: 15 April 2014 / Published: 24 April 2014
PDF Full-text (617 KB) | HTML Full-text | XML Full-text
Abstract
A crystallographic bar-joint framework, C in Rd, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω (C), is a singleton. Moreover, the
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A crystallographic bar-joint framework, C in Rd, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω (C), is a singleton. Moreover, the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function, ΦC(z), on the d-torus, Td, determined by a full rank translation symmetry group and an associated motif of joints and bars. Full article
(This article belongs to the Special Issue Rigidity and Symmetry)
Open AccessArticle Closed-Form Expressions for the Matrix Exponential
Symmetry 2014, 6(2), 329-344; doi:10.3390/sym6020329
Received: 28 February 2014 / Revised: 16 April 2014 / Accepted: 17 April 2014 / Published: 29 April 2014
Cited by 2 | PDF Full-text (330 KB) | HTML Full-text | XML Full-text
Abstract
We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to
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We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. We show the advantages of the method in comparison with standard approaches, especially when dealing with the exponential of low-dimensional matrices. In contrast to other approaches that require, e.g., solving differential equations, the present method only requires the construction of the inverse of the Vandermonde matrix. We show the advantages of the method by applying it to different cases, mostly restricting the calculational effort to the handling of two-by-two matrices. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
Open AccessArticle Dynamic Processes in Prochiral Solvating Agents (pro-CSAs) Studied by NMR Spectroscopy
Symmetry 2014, 6(2), 345-367; doi:10.3390/sym6020345
Received: 12 March 2014 / Revised: 7 May 2014 / Accepted: 7 May 2014 / Published: 14 May 2014
Cited by 3 | PDF Full-text (2656 KB) | HTML Full-text | XML Full-text
Abstract
Several dynamic processes, including tautomerism and macrocyclic inversion, in 1H-NMR prochiral solvating agents (pro-CSAs) are investigated. Various features of pro-CSA, including modes of interaction for complex formation, stoichiometry, binding strength and temperature effects were compared for three representative pro-CSA molecules. Structural effects
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Several dynamic processes, including tautomerism and macrocyclic inversion, in 1H-NMR prochiral solvating agents (pro-CSAs) are investigated. Various features of pro-CSA, including modes of interaction for complex formation, stoichiometry, binding strength and temperature effects were compared for three representative pro-CSA molecules. Structural effects of conjugated tetrapyrrole pro-CSA on the mechanism of enantiomeric excess determination are also discussed. Detailed analysis of species (complexes) and dynamic processes occurring in solution and their 1H-NMR spectral manifestations at various temperatures is presented. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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Open AccessArticle Symmetry Perspectives on Some Auxetic Body-Bar Frameworks
Symmetry 2014, 6(2), 368-382; doi:10.3390/sym6020368
Received: 15 January 2014 / Revised: 15 April 2014 / Accepted: 4 May 2014 / Published: 15 May 2014
Cited by 1 | PDF Full-text (290 KB) | HTML Full-text | XML Full-text
Abstract
Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied
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Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode. Full article
(This article belongs to the Special Issue Rigidity and Symmetry)
Open AccessArticle Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
Symmetry 2014, 6(2), 396-408; doi:10.3390/sym6020396
Received: 24 February 2014 / Revised: 12 May 2014 / Accepted: 14 May 2014 / Published: 22 May 2014
Cited by 3 | PDF Full-text (258 KB) | HTML Full-text | XML Full-text
Abstract
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry
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We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)

Review

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Open AccessReview Metalloporphyrin Symmetry in Chiral Recognition and Enantioselective Catalysis
Symmetry 2014, 6(2), 210-221; doi:10.3390/sym6020210
Received: 28 February 2014 / Revised: 31 March 2014 / Accepted: 1 April 2014 / Published: 10 April 2014
Cited by 5 | PDF Full-text (256 KB) | HTML Full-text | XML Full-text
Abstract
Symmetry plays a fundamental role in chiral recognition and enantioselective catalysis. Porphyrins possess a number of structural features that make them attractive for the stereocontrol of chiral recognition and metal-catalyzed asymmetric reactions. This article is a brief account of our studies on chiral
[...] Read more.
Symmetry plays a fundamental role in chiral recognition and enantioselective catalysis. Porphyrins possess a number of structural features that make them attractive for the stereocontrol of chiral recognition and metal-catalyzed asymmetric reactions. This article is a brief account of our studies on chiral recognition and enantioselective catalysis by optically active metalloporphyrins. Some of the studies on chiral recognition and asymmetric catalysis by metalloporphyrins performed by others have also been included when useful. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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Open AccessReview Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
Symmetry 2014, 6(2), 234-255; doi:10.3390/sym6020234
Received: 27 February 2014 / Revised: 31 March 2014 / Accepted: 11 April 2014 / Published: 17 April 2014
Cited by 1 | PDF Full-text (335 KB) | HTML Full-text | XML Full-text
Abstract
We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transformations. The deformation of the
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We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI) amplitudes (both on-shell and off-shell) can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
Open AccessReview Supramolecular Chirality in Porphyrin Chemistry
Symmetry 2014, 6(2), 256-294; doi:10.3390/sym6020256
Received: 18 March 2014 / Revised: 18 April 2014 / Accepted: 21 April 2014 / Published: 23 April 2014
Cited by 12 | PDF Full-text (1066 KB) | HTML Full-text | XML Full-text
Abstract
Supramolecular chirality, being an intelligent combination of supramolecular chemistry and chiral science, plays a decisive role in the functioning of various natural assemblies and has attracted much attention from the scientific community, due to different applications in modern technologies, medicine, pharmacology, catalysis and
[...] Read more.
Supramolecular chirality, being an intelligent combination of supramolecular chemistry and chiral science, plays a decisive role in the functioning of various natural assemblies and has attracted much attention from the scientific community, due to different applications in modern technologies, medicine, pharmacology, catalysis and biomimetic research. Porphyrin molecules are of particular interest to study this phenomenon owing to their unique spectral, physico-chemical and synthetic properties. This review highlights the most important types of chiral porphyrin structures by using the best-suited representative examples, which are frequently used in the area of supramolecular chirality. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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Open AccessReview Hydrodynamic Helical Orientations of Nanofibers in a Vortex
Symmetry 2014, 6(2), 383-395; doi:10.3390/sym6020383
Received: 15 April 2014 / Revised: 14 May 2014 / Accepted: 15 May 2014 / Published: 20 May 2014
Cited by 2 | PDF Full-text (1359 KB) | HTML Full-text | XML Full-text
Abstract
In this review article, I report our recent studies on spectroscopic visualizations of macroscopic helical alignments of nanofibers in vortex flows. Our designed supramolecular nanofibers, formed through self-assemblies of dye molecules, helically align in torsional flows of a vortex generated by mechanical rotary
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In this review article, I report our recent studies on spectroscopic visualizations of macroscopic helical alignments of nanofibers in vortex flows. Our designed supramolecular nanofibers, formed through self-assemblies of dye molecules, helically align in torsional flows of a vortex generated by mechanical rotary stirring of the sample solutions. The nanofiber, formed through bundling of linear supramolecular polymers, aligns equally in right- and left-handed vortex flows. However, in contrast, a one-handedly twisted nanofiber, formed through helical bundling of the supramolecular polymers, shows unequal helical alignments in these torsional flows. When the helical handedness of the nanofiber matches that of the vortex flow, the nanofiber aligns more efficiently in the flowing fluid. Such phenomena are observed not only with the artificial helical supramolecular nanofibers but also with biological nanofibers such as double-stranded DNA. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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Open AccessReview Symmetry Detection in Visual Impairment: Behavioral Evidence and Neural Correlates
Symmetry 2014, 6(2), 427-443; doi:10.3390/sym6020427
Received: 19 February 2014 / Revised: 13 May 2014 / Accepted: 14 May 2014 / Published: 26 May 2014
Cited by 1 | PDF Full-text (604 KB) | HTML Full-text | XML Full-text
Abstract
Bilateral symmetry is an extremely salient feature for the human visual system. An interesting issue is whether the perceptual salience of symmetry is rooted in normal visual development. In this review, we discuss empirical work on visual and tactile symmetry detection in normally
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Bilateral symmetry is an extremely salient feature for the human visual system. An interesting issue is whether the perceptual salience of symmetry is rooted in normal visual development. In this review, we discuss empirical work on visual and tactile symmetry detection in normally sighted and visually impaired individuals. On the one hand, available evidence suggests that efficient visual symmetry detection may need normal binocular vision development. On the other hand, converging evidence suggests that symmetry can develop as a principle of haptic perceptual organization in individuals lacking visual experience. Certain features of visual symmetry detection, however, such as the higher salience of the patterns containing a vertical axis of symmetry, do not systematically apply to the haptic modality. The neural correlates (revealed with neuroimaging) associated with visual and haptic symmetry detection are also discussed. Full article
(This article belongs to the Special Issue Visual Symmetry)
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Open AccessReview Chiral Liquid Crystals: Structures, Phases, Effects
Symmetry 2014, 6(2), 444-472; doi:10.3390/sym6020444
Received: 12 April 2014 / Revised: 5 June 2014 / Accepted: 10 June 2014 / Published: 16 June 2014
Cited by 18 | PDF Full-text (1632 KB) | HTML Full-text | XML Full-text
Abstract
The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of
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The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of supermolecular helicity, the occurrence of novel thermodynamic phases, as well as electro-optic effects which can only be observed in chiral liquid crystalline materials. In particular, I will discuss the formation of helical superstructures in cholesteric, Twist Grain Boundary and ferroelectric phases. As examples for the occurrence of novel phases the Blue Phases and Twist Grain Boundary phases are introduced. Chirality related effects are demonstrated through the occurrence of ferroelectricity in both thermotropic as well as lyotropic liquid crystals. Lack of mirror symmetry is also discussed briefly for some biopolymers such as cellulose and DNA, together with its influence on liquid crystalline behavior. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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Other

Jump to: Research, Review

Open AccessCase Report The Symmetric-Partitioning and Incremental-Relearning Classification and Back-Propagation-Network Tree Approach for Cycle Time Estimation in Wafer Fabrication
Symmetry 2014, 6(2), 409-426; doi:10.3390/sym6020409
Received: 12 March 2014 / Revised: 16 May 2014 / Accepted: 19 May 2014 / Published: 23 May 2014
Cited by 2 | PDF Full-text (398 KB) | HTML Full-text | XML Full-text
Abstract
An innovative classification and back-propagation-network tree (CABPN tree) approach is proposed in this study to estimate the cycle time of a job in a wafer fabrication factory, which is one of the most important tasks in controlling the wafer fabrication factory. The CABPN
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An innovative classification and back-propagation-network tree (CABPN tree) approach is proposed in this study to estimate the cycle time of a job in a wafer fabrication factory, which is one of the most important tasks in controlling the wafer fabrication factory. The CABPN tree approach is an extension from the traditional classification and regression tree (CART) approach. In CART, the cycle times of jobs of the same branch are estimated with the same value, which is far from accurate. To tackle this problem, the CABPN tree approach replaces the constant estimate with variant estimates. To this end, the cycle times of jobs of the same branch are estimated with a BPN, and may be different. In this way, the estimation accuracy can be improved. In addition, to determine the optimal location of the splitting point on a node, the symmetric partition with incremental re-learning (SP-IR) algorithm is proposed and illustrated with an example. The applicability of the CABPN tree approach is shown with a real case. The experimental results supported its effectiveness over several existing methods. Full article

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