Showing papers on "Symmetry (geometry) published in 1993"
28 Jun 1993
TL;DR: This work shows how to exploit symmetry in model checking for concurrent systems containing many identical or isomorphic components, and focuses in particular on those composed of many isomorphic processes.
Abstract: We show how to exploit symmetry in model checking for concurrent systems containing many identical or isomorphic components. We focus in particular on those composed of many isomorphic processes. In many cases we are able to obtain significant, even exponential, savings in the complexity of model checking.
412 citations
TL;DR: The methods described in this paper have been developed and tested for the recognition and tracking of cars in a real-time system for automatic car-following and headway control on normal roads.
Abstract: We present two methods for detecting mirror symmetry in images, one based directly on the intensity values and another one based on a discrete representation of local orientation. A symmetry finder has been developed which uses the intensity-based method to search an image for compact regions which display some degree of mirror symmetry due to intensity similarities across a straight axis. In a different approach, we look at symmetry as a bilateral relationship between local orientations. A symmetry-enhancing edge detector is presented which indicates edges dependent on the orientations at two different image positions. SEED, as we call it, is a detector element implemented by a feedforward network that holds the symmetry conditions. We use SEED to find the contours of symmetric objects of which we know the axis of symmetry from the intensity-based symmetry finder. The methods described in this paper have been developed and tested for the recognition and tracking of cars in a real-time system for automatic car-following and headway control on normal roads.
187 citations
TL;DR: Four experiments were designed in which Ss had to determine whether 2 symmetric or random patterns were the same regardless of possible affine transformations between them, providing mixed evidence on skewed symmetry in the perception of visual forms.
Abstract: Mathematically, skewed symmetry is a nonaccidental property because it can be interpreted as bilateral symmetry in depth viewed from a nonorthogonal angle. To find out whether this is a useful property in the perception of visual forms, 4 experiments were designed in which the Ss had to determine whether 2 symmetric or random patterns were the same regardless of possible affine transformations between them. The results provided mixed evidence: Although there was always a large symmetry advantage, skewed symmetry was only perceived as bilateral symmetry in depth for dot patterns with higher order types of symmetry (Experiment 1), when the dots were connected to form closed polygons (Experiments 2 and 4), or when they were surrounded by a frame to enhance their planarity (Experiment 3). In other cases, Ss relied on local groupings on the basis of proximity or curvilinearity, which are qualitatively affine invariant. Language: en
107 citations
TL;DR: The separable solutions of the fully nonlinear, convective dynamo with spherically symmetric buoyancy forces and boundary conditions arise from the group of symmetry operations that leave a rotating sphere unchanged; they are more general than the rather specialised solutions usually quoted in the geomagnetic literature as discussed by the authors.
94 citations
TL;DR: It is shown that the octree data structure supports these operations well, especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry.
Abstract: An algorithm for identifying symmetry of a 3-D object given by its octree is presented, and the symmetry degree (a measure of object symmetry) is proposed. The algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree. An object can be in an arbitrary position and with arbitrary orientation within the octree space, and a wide range of symmetries represented by groups of proper and improper rotations can be identified. It is shown that the octree data structure supports these operations well, especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry. The operation of the algorithm is illustrated using some synthetic test objects. The results, which are composed of identified symmetry types and the corresponding symmetry degrees, were satisfactory. >
84 citations
TL;DR: In this article, the structure of attractors for discrete equivariant dynamical systems was studied and the symmetry of an attractor was shown to be an arbitrary subgroup of the group of symmetries.
Abstract: We consider discrete equivariant dynamical systems and obtain results about the structure of attractors for such systems. We show, for example, that the symmetry of an attractor cannot, in general, be an arbitrary subgroup of the group of symmetries. In addition, there are group-theoretic restrictions on the symmetry of connected components of a symmetric attractor. The symmetry of attractors has implications for a new type of pattern formation mechanism by which patterns appear in the time-average of a chaotic dynamical system.
71 citations
TL;DR: Center of mass perception was investigated by varying the shape, size, and orientation of planar objects, and major axes tended to align with gravity in maximally symmetric objects.
Abstract: Center of mass perception was investigated by varying the shape, size, and orientation of planar objects. Shape was manipulated to investigate symmetries as information. The number of reflective symmetry axes, the amount of rotational symmetry, and the presence of radial symmetry were varied. Orientation affected systematic errors. Judgments tended to undershoot the center of mass. Random errors increased with size and decreased with symmetry. Size had no effect on random errors for maximally symmetric objects, although orientation did. The spatial distributions of judgments were elliptical. Distribution axes were found to align with the principle moments of inertia. Major axes tended to align with gravity in maximally symmetric objects. A functional and physical account was given in terms of the repercussions of error. Overall, judgments were very accurate.
60 citations
TL;DR: In this paper, the connection between the phase structure and the geometry of the renormalization group (RG) flow in systems with discrete parameter space symmetries is studied, and it is suggested that if the symmetry group is sufficiently large, i.e. an infinite discrete non-abelian group, then it may constrain the C-function so much that global (topological) information about the RG can be obtained.
56 citations
TL;DR: In this article, a global model of $q$-deformation for the quasi-orthogonal Lie algebras generating the groups of motions of the four-dimensional affine Cayley-Klein geometries is obtained starting from the three dimensional deformations.
Abstract: A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how the main algebraic classical properties of the CK systems can be implemented in the quantum case. Quantum deformed versions of either the space--time or space symmetry algebras (Poincar\'e (3+1), Galilei (3+1), 4D Euclidean as well as others) appear in this context as particular cases and several $q$-deformations for them are directly obtained.
51 citations
TL;DR: This paper introduces the concept of “index” of an element as part of the whole structure, which is the number, of its distinct symmetrical images, and introduces the rule for assembly to perform as usual, but to count each element as many times as its index.
Abstract: Symmetry, and related questions of group theory, especially representation theory, are well-known, popular topics among physicists. This paper describes how these classical ideas can be put to use in the realm of finite element computations by substituting a family of independent problems on a reduced domain (the “symmetry cell”) for the original problem on the whole domain. Two specific difficulties appear : one is how to set boundary conditions on symmetry planes (representation theory gives the answer); the other is how to proceed with the assembly of finite elements that constitute the symmetry cell. To deal with this, this paper introduces the concept of “index” of an element as part of the whole structure, which is the number, of its distinct symmetrical images. The rule for assembly then becomes to perform as usual, but to count each element as many times as its index.
TL;DR: In this paper, the crossing symmetry in Belavin's R-matrix was proved in the An-1(1) face model and a new family of L-operators for Belavin R matrices was constructed.
Abstract: Some algebraic structures in elliptic solutions of the Yang-Baxter equations are investigated. The author proves the crossing symmetry in Belavin's model (1981) as well as in the An-1(1) face model and constructs a new family of L-operators for Belavin's R-matrix as an application.
TL;DR: In this paper, a diagonals-parameter symmetry (DPS) model was proposed for the analysis of square contingency tables with ordered categories, which has a similar multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above.
Abstract: For the analysis of square contingency tables with ordered categories, Goodman (1979, Biometrika 66, 413-418) considered the diagonals-parameter symmetry (DPS) model, which has a multiplicative form for cell probabilities. This paper proposes another DPS model which has a similar multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above. Special cases of the proposed model include conditional symmetry and symmetry. The relationship with a stochastic ordering for marginal distributions is also described. Moreover, the relationships between the proposed model and the (generalized) palindromnic symmetry models are described. An example is given.
TL;DR: In this article, a safe and efficient algorithm for determination of symmetrically equivalent vertices, edges and faces in the corresponding molecular graph is outlined, and all fullerene isomers with up to 70 atoms are analyzed.
TL;DR: In this article, the rotational analysis of the 0-0 and 1-1 bands of the 5/2-7/2 and 3/2 -5/2 subbands of the CoO emission spectrum has been performed using a Fourier transform spectrometer.
11 May 1993
TL;DR: The authors discuss establishing a relationship between symmetry and two-fingered grasping of planar contours by constructing an appropriate description in terms of local reflectional and rotational symmetry.
Abstract: The authors discuss establishing a relationship between symmetry and two-fingered grasping of planar contours. Visual representations are chosen to meet the requirements of specified tasks such as object recognition or stereoscopic matching. When vision is regarded as a haptic sense, a new operational description is called for in support of dextrous manipulation. In the context of two-fingered grasp, an appropriate description can be constructed in terms of local reflectional and rotational symmetry. Related to symmetry-based representatons that have been used in pattern and object recognition, its structure is determined not heuristically, but precisely, by the nature of the grasping task. Its value is demonstrated by its incorporation into the control of a robot that can manipulate objects under visual guidance. >
15 Jun 1993
TL;DR: A continuous symmetry measure (CSM) is developed to evaluate symmetrics of shapes and objects and occluded shapes are reconstructed by locating the center of symmetry of the shape.
Abstract: Following the view that symmetry is a continuous feature, a continuous symmetry measure (CSM) is developed to evaluate symmetrics of shapes and objects. The symmetry measure is extended to evaluate the symmetry of occluded shapes. Using the symmetry measure, occluded shapes are reconstructed by locating the center of symmetry of the shape. >
TL;DR: In this article, it was shown that under perturbations which break the reflectional symmetry in O(2), the homoclinic cycle generically bifurcates to a quasi-periodic flow on a 2-torus.
Abstract: It has been known for several years that differential systems with O(2) symmetry can possess heteroclinic cycles between two equilibria which belong to the same group orbit. The author calls these objects 'homoclinic cycles' because they realize a homoclinic orbit from a group orbit of equilibria to itself. The author shows that under perturbations which break the reflectional symmetry in O(2), the homoclinic cycle generically bifurcates to a quasi-periodic flow on a 2-torus. The techniques applied to this problem are (i) the reduction of the system to the orbit space and (ii) a generalization of Melnikov's method for the study of perturbations of heteroclinic chains.
TL;DR: In this article, an extended version of the internal axis method was introduced to analyze the rotational spectrum of methanol to microwave accuracy, which was used for CH 3 OD in three lowest torsional levels (v t = 0, 1, 2).
TL;DR: In this article, the inverse of the strong symmetry of Jaulent-Miodek hierarchy is expressed explicitly by means of the solutions of the Shrodinger equation, and four new sets of symmetries are obtained after acting the inverse strong symmetry on three new seed symmetryes and one known seed symmetry.
Abstract: The inverse of the strong symmetry (recursion opterator) of Jaulent-Miodek hierarchy are expressed explicitly by means of the solutions of the Shrodinger equation. Four new sets of symmetries are obtained after acting the inverse strong symmetry on three new seed symmetryes and one known seed symmetry.
Journal Article•
TL;DR: Symmetry of information (in Kolmogorov complexity) is a concept that comes out of formalizing the idea of how much information about a string y is contained in a string x.
12 Feb 1993
TL;DR: The N-target decomposition as discussed by the authors is a unique and physically realizable decomposition, which is based on the concept of non-symmetric N-tors, i.e., the n-target which we separate out of the data has no symmetry (A N o equals 0).
Abstract: This leads to three world-views. One is the world of basic symmetry we live in, while the other is applicable to an exotic world where there is a preference for helices with right sense. The other exotic world caters to a world composed of helices with left sense. Hence we have arrived at a unique N-target decomposition which caters to the world of basic symmetry we live in. In this world it is still possible to have helices of any kind, but predominantly the symmetry is preferred, i.e., the N-target which we separate out of the data has no symmetry (A N o equals 0) and is completely non-symmetric (hence the name N-target). Other types of decomposition are based on eigenvalues and eigentargets. These are not transparent in general as to their physical significance. All these physically based arguments lead us to conclude that the N-target decomposition is unique and physically realizable in all cases.
TL;DR: In this paper, a simple geometrical model is used to derive symmetry operators and symmetry groups for molecules with three internal rotors and for homomolecular and heter-molecular trimers.
TL;DR: In this article, the authors give sufficient conditions for the tilings associated with an inflation rule to be uniquely ergodic under translations, the conditions holding for the pinwheel inflation rule.
Abstract: We discuss two new results on tilings of the plane. In the first, we give sufficient conditions for the tilings associated with an inflation rule to be uniquely ergodic under translations, the conditions holding for the pinwheel inflation rule. In the second result we prove there are matching rules for the pinwheel inflation rule, making the system the first known to have complete rotational symmetry.
TL;DR: A method is developed which exactly parameterizes the configurations of five membered rings, and generates distributions of q, P, S, and gamma for furanose rings in the structures of 665 nucleosides determined by X-ray crystallography.
Abstract: A method is developed which exactly parameterizes the configurations of five membered rings. In addition to the five bond lengths, (bj), four other parameters are needed to describe completely all configurations of a three-dimensional figure with five sides. Two of these parameters are taken as the phase angle, P, and amplitude, q (A), introduced by Cremer and Pople (J. Am. Chem. Soc. 97, 1354 (1975)) which give exactly the displacements of the atoms in any five-membered ring from a special plane (the CP plane). For the two other parameters, a second amplitude, S (A), and an orientation angle, gamma (the upper case Greek letter "gamma"), are introduced. These two new parameters describe the "distortion" of the projection of the ring in the CP plane. gamma is the angle in the CP plane at which the projected ring is maximally "spread" or "stretched," where the stretch is a least squares measure of position along a line through the ring center. S measures the difference between maximum stretch (in direction gamma) and minimum stretch (in direction gamma +/- 90 degrees) such that S = 0 denotes maximum symmetry. Transformations from Cartesian coordinates to the new internal coordinates, and from the new internal coordinates to the Cartesian set, are exact inverse transformations. Fortran source codes MAKERING and BREAKRING for these transformations are available. The set of four parameters aids in direct comparisons of ring structures and in detailed numerical analyses of data. They also aid the systematic generation of all possible rings, useful for theoretical studies of ring conformation. To demonstrate the descriptive method, we have generated distributions of q, P, S, and gamma for furanose rings in the structures of 665 nucleosides determined by X-ray crystallography.
01 Jan 1993
TL;DR: It is shown that it is possible to establish the point correspondences uniquely in the sense that they yield a unique affine structure of the object and that, the computation is possible in polynomial time.
Abstract: In this paper the problem of computing the point correspondences in a sequence of time-varying images of a 3D object undergoing nonrigid (affine) motion is addressed. It is assumed that the images are obtained through affine projections. The correspondences are established only from the analysis of the unknown 3D affine structure of the object, without making use of any attributes of the feature points. It is shown that it is possible to establish the point correspondences uniquely (up to symmetry) in the sense that they yield a unique affine structure of the object and that the computation is possible in polynomial time. Two different algorithms for computing the point correspondences are presented. Results on various real image sequences, including a sequence containing independently moving objects, demonstrate the applicability of the structure based approach to motion correspondence.