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Symmetry, Volume 6, Issue 1 (March 2014), Pages 1-163

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Editorial

Jump to: Research, Review

Open AccessEditorial Acknowledgement to Reviewers of Symmetry in 2013
Symmetry 2014, 6(1), 89; doi:10.3390/sym6010089
Received: 24 February 2014 / Accepted: 24 February 2014 / Published: 24 February 2014
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Abstract The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2013. [...] Full article

Research

Jump to: Editorial, Review

Open AccessArticle Peripheral Contour Grouping and Saccade Targeting: The Role of Mirror Symmetry
Symmetry 2014, 6(1), 1-22; doi:10.3390/sym6010001
Received: 26 September 2013 / Revised: 30 December 2013 / Accepted: 30 December 2013 / Published: 2 January 2014
Cited by 3 | PDF Full-text (558 KB) | HTML Full-text | XML Full-text
Abstract
Integrating shape contours in the visual periphery is vital to our ability to locate objects and thus make targeted saccadic eye movements to efficiently explore our surroundings. We tested whether global shape symmetry facilitates peripheral contour integration and saccade targeting in three [...] Read more.
Integrating shape contours in the visual periphery is vital to our ability to locate objects and thus make targeted saccadic eye movements to efficiently explore our surroundings. We tested whether global shape symmetry facilitates peripheral contour integration and saccade targeting in three experiments, in which observers responded to a successful peripheral contour detection by making a saccade towards the target shape. The target contours were horizontally (Experiment 1) or vertically (Experiments 2 and 3) mirror symmetric. Observers responded by making a horizontal (Experiments 1 and 2) or vertical (Experiment 3) eye movement. Based on an analysis of the saccadic latency and accuracy, we conclude that the figure-ground cue of global mirror symmetry in the periphery has little effect on contour integration or on the speed and precision with which saccades are targeted towards objects. The role of mirror symmetry may be more apparent under natural viewing conditions with multiple objects competing for attention, where symmetric regions in the visual field can pre-attentively signal the presence of objects, and thus attract eye movements. Full article
(This article belongs to the Special Issue Visual Symmetry)
Open AccessArticle Symmetry-Breaking in a Rate Model for a Biped Locomotion Central Pattern Generator
Symmetry 2014, 6(1), 23-66; doi:10.3390/sym6010023
Received: 28 October 2013 / Revised: 13 December 2013 / Accepted: 13 December 2013 / Published: 3 January 2014
Cited by 1 | PDF Full-text (4654 KB) | HTML Full-text | XML Full-text
Abstract
The timing patterns of animal gaits are produced by a network of spinal neurons called a Central Pattern Generator (CPG). Pinto and Golubitsky studied a four-node CPG for biped dynamics in which each leg is associated with one flexor node and one [...] Read more.
The timing patterns of animal gaits are produced by a network of spinal neurons called a Central Pattern Generator (CPG). Pinto and Golubitsky studied a four-node CPG for biped dynamics in which each leg is associated with one flexor node and one extensor node, with Ζ2 x Ζ2 symmetry. They used symmetric bifurcation theory to predict the existence of four primary gaits and seven secondary gaits. We use methods from symmetric bifurcation theory to investigate local bifurcation, both steady-state and Hopf, for their network architecture in a rate model. Rate models incorporate parameters corresponding to the strengths of connections in the CPG: positive for excitatory connections and negative for inhibitory ones. The three-dimensional space of connection strengths is partitioned into regions that correspond to the first local bifurcation from a fully symmetric equilibrium. The partition is polyhedral, and its symmetry group is that of a tetrahedron. It comprises two concentric tetrahedra, subdivided by various symmetry planes. The tetrahedral symmetry arises from the structure of the eigenvalues of the connection matrix, which is involved in, but not equal to, the Jacobian of the rate model at bifurcation points. Some of the results apply to rate equations on more general networks. Full article
(This article belongs to the Special Issue Symmetry Breaking)
Open AccessArticle On General Off-Shell Representations of World Line (1D) Supersymmetry
Symmetry 2014, 6(1), 67-88; doi:10.3390/sym6010067
Received: 19 December 2013 / Revised: 20 January 2014 / Accepted: 22 January 2014 / Published: 3 February 2014
Cited by 5 | PDF Full-text (1193 KB) | HTML Full-text | XML Full-text
Abstract
Every finite-dimensional unitary representation of the N-extended world line supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets that are identifiable with representations of the Clifford algebra. The data [...] Read more.
Every finite-dimensional unitary representation of the N-extended world line supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets that are identifiable with representations of the Clifford algebra. The data specifying this procedure is a sequence of subspaces of the direct sum of Adinkras, which then opens an avenue for the classification of the continuum of the so-constructed off-shell supermultiplets. Full article
(This article belongs to the Special Issue Supersymmetry 2014)
Open AccessArticle Using Symmetries (Beyond Geometric Symmetries) in Chemical Computations: Computing Parameters of Multiple Binding Sites
Symmetry 2014, 6(1), 90-102; doi:10.3390/sym6010090
Received: 9 May 2013 / Revised: 18 February 2014 / Accepted: 21 February 2014 / Published: 25 February 2014
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Abstract
We show how transformation group ideas can be naturally used to generate efficient algorithms for scientific computations. The general approach is illustrated on the example of determining, from the experimental data, the dissociation constants related to multiple binding sites. We also explain [...] Read more.
We show how transformation group ideas can be naturally used to generate efficient algorithms for scientific computations. The general approach is illustrated on the example of determining, from the experimental data, the dissociation constants related to multiple binding sites. We also explain how the general transformation group approach is related to the standard (backpropagation) neural networks; this relation justifies the potential universal applicability of the group-related approach. Full article
(This article belongs to the Special Issue Chemical Applications of Symmetry)
Open AccessArticle Pseudo Hermitian Interactions in the Dirac Equation
Symmetry 2014, 6(1), 103-110; doi:10.3390/sym6010103
Received: 31 July 2013 / Revised: 18 December 2013 / Accepted: 23 December 2013 / Published: 17 March 2014
Cited by 3 | PDF Full-text (229 KB) | HTML Full-text | XML Full-text
Abstract
We consider a (2 + 1)-dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states, and the Dirac Hamiltonians are η-pseudo Hermitian. Some examples have [...] Read more.
We consider a (2 + 1)-dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states, and the Dirac Hamiltonians are η-pseudo Hermitian. Some examples have been explicitly worked out. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)

Review

Jump to: Editorial, Research

Open AccessReview The Hunt for Supersymmetry at the Tevatron
Symmetry 2014, 6(1), 111-147; doi:10.3390/sym6010111
Received: 30 December 2013 / Accepted: 17 February 2014 / Published: 19 March 2014
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Abstract
During the Tevatron data-taking period from April 2001 to September 2011 (Run-II), several searches for supersymmetric particles were performed. The results from searches by the CDF and DØ collaborations are concisely reviewed. This includes results up to the summer conferences of 2013. [...] Read more.
During the Tevatron data-taking period from April 2001 to September 2011 (Run-II), several searches for supersymmetric particles were performed. The results from searches by the CDF and DØ collaborations are concisely reviewed. This includes results up to the summer conferences of 2013. Model-independent and model-dependent limits on new particle production are set, and interpretations in supersymmetric models are given. Several limits from the Large Electron Positron (LEP) era have been extended. Specific results are placed into the context of the Tevatron performance expectations and a few of the current results from searches at the Large Hadron Collider (LHC). Full article
(This article belongs to the Special Issue Supersymmetry 2014)
Open AccessReview Symmetry Aspects of Dislocation-Effected Crystal Properties: Material Strength Levels and X-ray Topographic Imaging
Symmetry 2014, 6(1), 148-163; doi:10.3390/sym6010148
Received: 21 January 2014 / Revised: 24 February 2014 / Accepted: 12 March 2014 / Published: 20 March 2014
Cited by 2 | PDF Full-text (1355 KB) | HTML Full-text | XML Full-text
Abstract
Several materials science type research topics are described in which advantageous use of crystal symmetry considerations has been helpful in ferreting the essential elements of dislocation behavior in determining material properties or for characterizing crystal/polycrystalline structural relationships; for example: (1) the mechanical [...] Read more.
Several materials science type research topics are described in which advantageous use of crystal symmetry considerations has been helpful in ferreting the essential elements of dislocation behavior in determining material properties or for characterizing crystal/polycrystalline structural relationships; for example: (1) the mechanical strengthening produced by a symmetrical bicrystal grain boundary; (2) cleavage crack formation at the intersection within a crystal of symmetrical dislocation pile-ups; (3) symmetry aspects of anisotropic crystal indentation hardness measurements; (4) X-ray diffraction topography imaging of dislocation strains and subgrain boundary misorientations; and (5) point and space group aspects of twinning. Several applications are described in relation to the strengthening of grain boundaries in nanopolycrystals and of multiply-oriented crystal grains in polysilicon photovoltaic solar cell materials. A number of crystallographic aspects of the different topics are illustrated with a stereographic method of presentation. Full article
(This article belongs to the Special Issue Crystal Symmetry and Structure)

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