Showing papers on "Symmetry (geometry) published in 2012"
TL;DR: A complete classification of two-band k·p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry is performed and the existence of new 3D topological semimetal characterized by C(4,6)-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C( 6)-protected triple-Wey nodes with cubic in- plane dispersion is
Abstract: We perform a complete classification of two-band k . p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by C-4,C-6-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C-6-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr2Se4 and confirm it is a double-Weyl metal protected by C-4 symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001] axis to the [111] axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group S-6 of that phase. Finally, we discuss experimentally relevant effects including the splitting of multi-Weyl nodes by applying a C-n breaking strain and the surface Fermi arcs in these new semimetals.
544 citations
TL;DR: In this article, a spectral curve describing torus knots and links in the B-model is proposed, which is obtained by exploiting the full Sl(2;Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knot in the large N Gopakumar{Vafa duality.
Abstract: We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2;Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar{Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.
224 citations
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TL;DR: In this article, a prescription to compute the superconformal index for all theories of class S was proposed, and a simple criterion for the given theory of S to have a decoupled free component and for it to have enhanced flavor symmetry was derived.
Abstract: Recently a prescription to compute the superconformal index for all theories of class S was proposed In this paper we discuss some of the physical information which can be extracted from this index We derive a simple criterion for the given theory of class S to have a decoupled free component and for it to have enhanced flavor symmetry Furthermore, we establish a criterion for the "good", the "bad", and the "ugly" trichotomy of the theories After interpreting the prescription to compute the index with non-maximal flavor symmetry as a residue calculus we address the computation of the index of the bad theories In particular we suggest explicit expressions for the superconformal index of higher rank theories with E_n flavor symmetry, ie for the Hilbert series of the multi-instanton moduli space of E_n
127 citations
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TL;DR: The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group as mentioned in this paper, and the symmetry rank of a smooth closed manifold admits a positively curved metric with maximal symmetry rank.
Abstract: The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.
98 citations
TL;DR: The concept of bilateral reflection symmetry to curved glide-reflection symmetry in 2D euclidean space is generalized, such that classic reflection symmetry becomes one of its six special cases, and a local feature-based approach for curved gliding symmetry detection from real, unsegmented 2D images is proposed.
Abstract: We generalize the concept of bilateral reflection symmetry to curved glide-reflection symmetry in 2D euclidean space, such that classic reflection symmetry becomes one of its six special cases. We propose a local feature-based approach for curved glide-reflection symmetry detection from real, unsegmented 2D images. Furthermore, we apply curved glide-reflection axis detection for curved reflection surface detection in 3D images. Our method discovers, groups, and connects statistically dominant local glide-reflection axes in an Axis-Parameter-Space (APS) without preassumptions on the types of reflection symmetries. Quantitative evaluations and comparisons against state-of-the-art algorithms on a diverse 64-test-image set and 1,125 Swedish leaf-data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent, respectively, and superior performance over existing reflection symmetry detection algorithms. Potential applications in computer vision, particularly biomedical imaging, include saliency detection from unsegmented images and quantification of deviations from normality. We make our 64-test-image set publicly available.
85 citations
TL;DR: In this article, the complete preliminary group classification of a class of nonlinear wave equations was carried out via the classification of one-dimensional Lie symmetry extensions related to a fixed finite-dimensional subalgebra of the equivalence algebra of the class under consideration.
Abstract: Preliminary group classification became a prominent tool in the symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi, and Valenti [J. Math. Phys. 32, 2988–2995 (1991)10.1063/1.529042]. In this paper the partial preliminary group classification of a class of nonlinear wave equations was carried out via the classification of one-dimensional Lie symmetry extensions related to a fixed finite-dimensional subalgebra of the infinite-dimensional equivalence algebra of the class under consideration. In the present paper we implement the complete group classification of the same class up to both usual and general point equivalence using the algebraic method of group classification. This includes the complete preliminary group classification of the class and finding those Lie symmetry extensions which are not associated with subalgebras of the equivalence algebra. The complete preliminary group classification is based on listing all inequivalent subalgebras of the whole infinite-dimensi...
69 citations
TL;DR: In this paper, the basic theory of semidefinite programs with symmetry is described and applications from coding theory, combinatorics, geometry, and polynomial optimization are discussed.
Abstract: This chapter provides the reader with the necessary background for dealing with semidefinite programs which have symmetry. The basic theory is given and it is illustrated in applications from coding theory, combinatorics, geometry, and polynomial optimization.
64 citations
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23 Sep 2012
TL;DR: This paper presents a meta-modelling framework for graph-based configuration analysis that automates the very labor-intensive and therefore time-heavy and expensive process of manually selecting configuration parameters.
Abstract: Preface.- Introduction.- Graphs.- Groups, Actions, and Symmetry.- Maps.- Combinatorial Configurations.- Geometric Configurations.- Index.- Bibliography.
62 citations
TL;DR: A novel method to characterize 3D surfaces through the computation of a function called (multiscale) area projection transform, measuring the likelihood of points in the 3D space to be center of radial symmetry at selected scales (radii).
Abstract: We present a novel method to characterize 3D surfaces through the computation of a function called (multiscale) area projection transform, measuring the likelihood of points in the 3D space to be center of radial symmetry at selected scales (radii). The function is derived through a simple geometric framework based on parallel surfaces and can be easily computed on triangulated meshes. It measures locally the area of the surface well approximated by a sphere of radius R centered in the point and can be normalized in order to obtain a scale invariant radial symmetry enhancement transform. This transform can therefore be used to detect and characterize salient regions like approximately spherical and approximately cylindrical surface parts and, being robust against holes and missing parts, it is suitable for real world applications e.g. anatomical features detection. Furthermore, its histograms can be effectively used to build a global shape descriptor that provides very good results in shape retrieval experiments. © 2012 Wiley Periodicals, Inc.
60 citations
TL;DR: A procedure for the systematic search and identification of the symmetries of 2D and 3D structural configurations, and hence for the automatic recognition of the symmetry group to be used in a group-theoretic analysis of the system.
54 citations
01 Nov 2012
TL;DR: An algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region, is presented.
Abstract: We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape. Since different point pairs can share a common point, shape regions covered by points in different scale clusters can overlap. We introduce the symmetry scale matrix (SSM), where each entry estimates the likelihood two point pairs belong to symmetries at the same scale. The pair-to-pair symmetry affinity is computed based on a pair signature which encodes scales. We perform spectral clustering using the SSM to obtain the scale clusters. Then for all points belonging to the same scale cluster, we perform the second-level spectral clustering, based on a novel point-to-point symmetry affinity measure, to extract partial symmetries at that scale. We demonstrate our algorithm on complex shapes possessing rich symmetries at multiple scales.
TL;DR: In this article, the generalized symmetry classification of polylinear autonomous discrete equations defined on the square is carried out, which belong to a twelve-parametric class, and the direct result of this classification is a list of equations containing no new examples.
Abstract: We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result of this classification is a list of equations containing no new examples. However, as an indirect result of this work we find a number of integrable examples pretending to be new. One of them has a nonstandard symmetry structure, the others are analogues of the Liouville equation in the sense that they are Darboux integrable. We also enumerate all equations of the class, which are linearizable via a two-point first integral, and specify the nature of integrability of some known equations.
TL;DR: In this paper, the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity was studied using generalised geometry, and it was shown that uncharged black M2-branes become charged under Uduality, generalising the Harrison transformation.
Abstract: Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and SL(5) U-duality groups reduce to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.
TL;DR: In this paper, infinite translation surfaces with Z-covers of compact translation surfaces were studied and conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and gave a necessary and sufficient condition for recurrence of their straight line flows.
Abstract: We study infinite translation surfaces which are Z-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithusen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.
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TL;DR: In this article, the authors present a survey covering selected developments since 1999 to 2011 dealing with the construction of Einstein metrics on bundles and Einstein metrics with symmetries, which is a sequel to the survey given by the author in Surveys in Differential Geometry Vol. 6 in 1999.
Abstract: This is a sequel to the survey given by the author in Surveys in Differential Geometry Vol. 6 in 1999. The present survey covers selected developments since 1999 to 2011 dealing with the construction of Einstein metrics on bundles and Einstein metrics with symmetries.
TL;DR: A simple model using a description of the d orbitals with trigonal symmetry that along with the application of the spin-orbit interaction successfully explains the magnetic properties of high-spin d(4,6) complexes with three- and four-coordinate geometry.
Abstract: There have been a number of recent studies reporting high-spin d4,6 complexes with three- and four-coordinate geometry, which exhibit roughly trigonal symmetry. These include complexes of Fe(II) wi...
TL;DR: An algorithmic framework allowing for fast and elegant path correction exploiting Lie group symmetries and operating without the need for explicit control strategies such as cross-track regulation is developed.
Abstract: In this paper we develop an algorithmic framework allowing for fast and elegant path correction exploiting Lie group symmetries and operating without the need for explicit control strategies such as cross-track regulation. These systems occur across the gamut of robotics, notably in locomotion, be it ground, underwater, airborne, or surgical domains. Instead of reintegrating an entire trajectory, the method selectively alters small key segments of an initial trajectory in a consistent way so as to transform it via symmetry operations. The algorithm is formulated for arbitrary Lie groups and applied in the context of the special Euclidean group and subgroups thereof. A sampling-based motion planner is developed that uses this method to create paths for underactuated systems with differential constraints. It is also shown how the path correction method acts as a controller within a feedback control loop for real-time path correction. These approaches are demonstrated for ground vehicles in the plane and for flexible bevel tip needle steering in space. The results show that using symmetry-based path correction for motion planning provides a prudent and simple, yet computationally tractable, integrated planning and control strategy.
TL;DR: In this paper, the generalized symmetry classification of polylinear autonomous discrete equations defined on the square is carried out, which belong to a twelve-parametric class, and the direct result of this classification is a list of equations containing no new examples.
Abstract: We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result of this classification is a list of equations containing no new examples. However, as an indirect result of this work we find a number of integrable examples pretending to be new. One of them has a nonstandard symmetry structure, the others are analogues of the Liouville equation in the sense that those are Darboux integrable. We also enumerate all equations of the class, which are linearizable via a two-point first integral, and specify the nature of integrability of some known equations.
01 Mar 2012
TL;DR: A possible extension of the Shubnikov approach may be developed in the sense of Magnetic Superspace Groups as in crystallographic incommensurate structures as discussed by the authors, which may be a better approach when macroscopic properties have to be deduced from the spin configurations.
Abstract: The crystallographic approach to magnetic structures is largely based on two kinds of descriptions: symmetry invariance of magnetic configurations (Magnetic Space Groups, often called Shubnikov groups) and group representation theory applied to conventional crystallographic space groups. The first approach is nearly exclusively used for the case of commensurate magnetic structures and usually is limited to a description of the invariance symmetry properties for this kind of configurations [1–5]. The representation analysis is more general and can be applied to all kinds of magnetic structures. The literature on this field is broad and one can consult the papers of E.F. Bertaut [6–9] and Y. Izyumov and co-workers [10–15] to get a deeper insight into the problem. A possible extension of the Shubnikov approach may be developed in the sense of Magnetic Superspace Groups as in crystallographic incommensurate structures. This more general approach extends the invariance concept to incommensurate magnetic structures and may be a better approach when macroscopic properties have to be deduced from the spin configurations. At present not too much work has been done in that sense so it will not be considered in the present notes.
01 Jan 2012
TL;DR: In this paper, the authors considered the Dirichlet boundary condition on a given positive function that is invariant under all (Euclidean) symmetries of the square.
TL;DR: In this paper, a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain was found, and it was shown that this symmetry originates from the quantum superalgebra, and in the rational limit exactly reproduces the secret symmetrization of the AdS/CFT worldsheet Smatrix.
Abstract: We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra , and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix.
TL;DR: In this article, a generalized chiral decomposition of the center-of-mass motion was derived for the Earth-Moon-Sun system. But this decomposition is based on the Bargmann framework.
Abstract: Hill's equations, which first arose in the study of the Earth-Moon-Sun system, admit the two-parameter centrally extended Newton-Hooke symmetry without rotations. This symmetry allows for extending Kohn's theorem about the center-of-mass decomposition. Particular light is shed on the problem using Duval's "Bargmann" framework. The separation of the center-of-mass motion into that of a guiding center and relative motion is derived by a generalized chiral decomposition.
TL;DR: The purpose of this paper is to describe a phyllotactic organization of points through its Voronoi cells and Delaunay triangulation and to refer to the concept of defects developed in condensed matter physics.
Abstract: Phyllotaxis, the search for the most homogeneous and dense organizations of small discs inside a large circular domain, was first developed to analyse arrangements of leaves or florets in plants. It has since become an object of study not only in botany, but also in mathematics, computer simulations and physics. Although the mathematical solution is now well known, an algorithm setting out the centres of the small discs on a Fermat spiral, the very nature of this organization and its properties of symmetry remain to be examined. The purpose of this paper is to describe a phyllotactic organization of points through its Voronoi cells and Delaunay triangulation and to refer to the concept of defects developed in condensed matter physics. The topological constraint of circular symmetry introduces an original inflation–deflation symmetry taking the place of the translational and rotational symmetries of classical crystallography.
TL;DR: This paper considers the use of the whole-sample symmetric boundary conditions in image restoration, and a technique of Kronecker product approximations was successfully applied to restore images with the zero BCs, half- sample symmetric BCs and anti-reflexive BCs.
TL;DR: The idea of a maniplex, a common generalization of map and of polytope, is introduced and operators, orientability, symmetry and the action of the symmetry group are discussed.
Abstract: This paper introduces the idea of a maniplex, a common generalization of map and of polytope. The paper then discusses operators, orientability, symmetry and the action of the symmetry group.
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14 Oct 2012
TL;DR: In this article, the authors give two proofs based on the geometry of the Fubini-Study metric that any symmetry of a quantum system is unitary or anti-nitary.
Abstract: Wigner's theorem asserts that any symmetry of a quantum system is unitary or antiu- nitary. In this short note we give two proofs based on the geometry of the Fubini-Study metric.
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TL;DR: In this paper, the authors classify closed, simply connected (n)-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions 2.
Abstract: We classify closed, simply connected $n$-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $2\leq n\leq 6$. In dimensions $3k$, $k=1,2$ there is only one such manifold and it is diffeomorphic to the product of $k$ copies of the 3-sphere.
TL;DR: Detailed analysis of the subgroup lattice structure of the dihedral group D4 and of the octahedral group to complete classification by symmetry type of those in ranks 3 and 4 is provided.
Abstract: We derive some general results on the symmetries of equivelar toroids and provide detailed analysis of the subgroup lattice structure of the dihedral group D4 and of the octahedral group to complete classification by symmetry type of those in ranks 3 and 4.