Symmetric Figures Research Articles

Tuning to Y-like figures in the cat striate neurons

Sensitivity to symmetric or asymmetric Y-like figures and crosses of different shapes and orientations flashed in the receptive field was studied in 101 neurons of the cat striate cortex (area 17) and compared with their orientation tuning to a single light bar. Selective sensitivity to the Y-like figure (figure/bar response ratio more than 1.25) was found in 78/101 neurons (77.2% of cases) and to the cross—in 54/101 units (53.4%). In 62.5% of neurons with sensitivity to both figures, sensitivity to the Y-like figure was higher than to a cross. Tuning to Y-like figure was typically (60%) selective to both its shape and orientation. The remaining Y-like selective neurons exhibited invariant tuning to orientation and/or shape of the figure. The preferred angles between two lines of Y-like figures were distributed in the range of 22.5–157.5° with slight preference to 90°, while crosses of 45° and 90° angles were preferable. Response magnitudes to a single bar, a Y-like figure and a cross were positively correlated. Possible mechanisms and functional implication of the striate sensitivity to Y-like figures are discussed.

The effect of symmetry on the recognition accuracy of patterns of different complexity

Symmetry is one of the most important determinants of visual perception. The influence of pattern symmetry on their recognition accuracy was investigated in the psychophysical experiment on human subjects under the conditions of backward masking. A rectangular frame of twelve line segments of equal length was used as a masking pattern (MP). The test patterns (TPs), nonverbal figures were the parts of MP composed by joining four, six, or eight line segments. Five figure sets consisting of equal number of symmetrical and asymmetrical figures of different complexity were used in the experiment. TP was presented for 10 ms, followed by MP for 500 ms with interstimulus interval, which was established for each subject individually as the shortest interval permitting 50-90 proc. recognition accuracy. Each subject took part in four to six test trial sessions. In each trial session, the equal number of symmetrical and asymmetrical figures composed by the same number of line segments was presented for recognition.Experimental data have demonstrated that effect of symmetry on pattern recognition depends on the number of pattern components. The asymmetrical figures consisting of four and six line segments were recognised more accurately than symmetrical ones, whereas the asymmetrical figures consisting of eight line segments have had the lower recognition accuracy than symmetrical ones. Experimental results were interpreted on the basis of optimal relation between the number of elements and symmetry that enables the greatest recognition probability of visual patterns.

Direction information coordinated via the posterior third of the corpus callosum during bimanual movements.

We examined bimanual coordination in a patient before and after each stage of callosotomy surgery. We tested how well the patient coordinated movement direction between the hands. The patient drew symmetrical or asymmetrical figures simultaneously with both hands. Before surgery, symmetrical figures were drawn well and asymmetrical figures were drawn poorly. Following anterior callosotomy, the drawings improved slightly. Symmetrical figures were still drawn well, and asymmetrical ones were still drawn poorly. Thus, spatial integration remained intact despite the loss of interhemispheric communication between frontal cortical sites. After posterior callosotomy, spatial coordination deteriorated significantly. Mirror-image drawings became less symmetrical, while asymmetrical drawings improved. These data indicate that the posterior callosum mediates the coordination of direction information between the hands during bimanual movements. Given the topographical organization of the corpus callosum, this integration is likely carried out by parietal cortex.

"Invertible" Polyhedron Models.

We recently discovered the existence of some polyhedral models originating in what was once East Germany and we would like to call them to the attention of enthusiasts of polyhedral geometry who may not have discovered them yet. The seven models are large-suitable for demonstrations to groups of students and mathematicians-colorful and meticulously constructed with cloth hinges at the edges. Moreover, some have internal magnets allowing for easy transformation from one state to another. The models, all Platonic solids in their original state, are each decomposable into pieces that can be reassembled to form stellations having the same underlying symmetry as the original polyhedron. The process of transforming them is a kinetic process with interesting intermediate states. And, in almost any state, they are stunningly beautiful. There is no standard language of which we are aware to describe the kinds of dissections involved, though there is a literature on these polyhedra, albeit, it seems, only in German. One such booklet is Umstiilpmnodelle derPlatonische Korper, by Wolfgang Maas and Immo Sykora, published by Kaspar Hauser Therapeutikum, Berlin, 1993. The language we use is, we hope, descriptive, but it may not appear standard even to experienced geometers. With the exception of one of the three cubes, these seven models of the Platonic solids all have the characteristic that when they are disassembled they come apart into three or more pieces so that the original polyhedron can be turned inside out, leaving a cavity in the shape of the original polyhedron. To be more precise, the models are constructed so that the pyramids (whose bases are the faces of the original polyhedron, with height equal to the perpendicular distance from the center of the base face to the center of the polyhedron) can be repositioned pointing outwards, rather than inwards. On some of the models the pyramids are partitioned into parts, apparently so they can be maneuvered properly. We will refer to these models, with the exception of the unusual cube, as invertible polyhedra. There are two features shared by all the invertible models. The first is that the coloring of the original solid destroys the symmetry of the underlying group, reducing the symmetry group of the polyhedron to a cyclic or dihedral group-or worse, to a centrally symmetric figure. However, in each case, when the polyhedron is reassembled in its inverted form its surface is monochromatic so that the entire symmetry group of the underlying polyhedron is again revealed: A4 for the tetrahedron, S4 for the cube and octahedron, and A5 for the dodecahedron and icosahedron. This feature, with the color of the inverted model being always

Aligning symmetric and asymmetric top molecules via single photon excitation

The theory developed by Zare [Ber. Bunsenges. Phys. Chem. 86, 422 (1982)] for using electric-dipole-allowed photoexcitation with linearly polarized light to align linear and symmetric top molecules via parallel transitions is extended to include perpendicular transitions, as well as the alignment of asymmetric tops via a-, b-, or c-type transitions. Analytical expressions for the spatial distribution of a symmetric top figure axis following a parallel or perpendicular transition are presented. A prescription is developed for determining the spatial distribution of each principal axis of an asymmetric or symmetric top following parallel or perpendicular type transitions. The degree of alignment obtainable via photoexcitation for symmetric and asymmetric tops is discussed, with the somewhat surprising result that all three principal axes of an asymmetric top can be highly aligned via photoexcitation. A simple computer program for calculating the degree of alignment of each principal axis of a symmetric or asymmetric top following an a-, b-, or c-type transition is described and made available.

Principles and methods of quantitative analysis onb-axis disorder in 2:1 dioctahedral phyllosilicate

IN XRD patterns of clay minerals, a phenomenon that strong peaks often have (00 l ) and ( hkl ) ( k =3 n ) indices and show symmetric figures can be seen commonly, while a minorityof reflection peaks ( hkl ) ( k ≠3 n ) are comparatively weak and wide, and show asymmetric...

Analysis of torso movement of trans-femoral amputees during level walking.

The purpose of this study is to analyze the movement of unilateral trans-femoral amputees' gait and find patterns of compensated movement to accommodate the loss of locomotor power on one side. A 3-D analyzer system and force plate were used to measure 12 amputees. The main focus was to find characterized movement particularly of the upper body such as pelvis, shoulder and arms. It was Saunders et al. (1953), who said that the human body can be purposely divided into two subsystems in analyzing man's locomotion. This study, however is not to measure the level of function, but to evaluate the appearance of gait. Twelve markers were placed on the subjects, and two locations for measuring points were used to measure movement of the torso in three axis (X, Y, Z) without measuring the position of the centre of gravity. The two points were at shoulder level, and at pelvic level. Lissajou's figure was used to evaluate the movements at these two marks. The quality of the gait was determined through subjective evaluation by the author. Determination was made on two factors, one from observing the gait of the amputees and the other, patterns from their Lissajou's figure of two measuring points. Then they were categorized as good walker or "other". Good walkers had results at shoulder level which were closer to the symmetrical Lissajou's figure of normal walkers. Yet the symmetrical pattern was not present at the pelvis level for the good walker.

Characteristics of Combined Propulsion, Levitation and Guidance System with Asymmetric Figure between Upper and Lower Coils in EDS.

In commercializing the superconducting maglev system it is important to reduce the cost, especially that of ground coils constructed along the whole length of the guideway. For a system to save the cost, we have examined the combined propulsion, levitation and guidance system (PLG system) which can generate levitation, guidance and propulsion forces by the same ground coils. This system is composed of superconducting coils on board and 8-shaped ground coils on the side wall of the guideway whose unit coils are connected reversely between the upper and lower sides and between the right and left sides to make null flux circuits, and serially between the front and rear sides to make a three phase circuit with the power source. On the contrary, the EDS (Electro-Dynamic Suspension) maglev including the PLG system needs auxiliary wheels at low speed at which the levitation force and the electromagnetic stiffness are insufficient for non-contact running. The take off velocity is desirably made as low as possible for dispensing with the strength design and maintenance of track and wheels. Since the side wall levitation system has a large coupling between guidance and rolling, it is important to improve the stiffness considering this coupling, which restricts the take off velocity. The ground coils in the above-mentioned examination have symmetric figure and same impedance between upper and lower coils. This paper describes the PLG system with asymmetric figure between upper and lower coils which reduce the large coupling between guidance and rolling and increase the guidance stiffness. We present not only the principle but also the characteristics of this system with a numerical example and a test run at Miyazaki test track.

Clusters of inert gases of the close packed structures

This analysis shows that a short-range interaction potential approximates parameters of inert gas crystals better than the Lennard-Jones one. A method is developed for calculation of the atom binding energy of clusters of the face-centered cubic (fcc) and hexagonal structure. It uses the short-range character of interaction of atoms that leads to interaction between nearest neighbors of the cluster only. Symmetric figures of these clusters with magic numbers of atoms are considered. Energies of clusters of fcc, hexagonal and icosahedral structures are compared for a short-range interaction between atoms.

Phyllosilicate preferred orientation in relation to strain path determination in the lower Paleozoic Stavelot-Venn Massif (Ardennes, Belgium)

Phyllosilicate preferred orientation, measured by means of an X-ray pole figure goniometer, allows a quantitative exploration of the slaty cleavage development. The relationship between phyllosilicate preferred orientation and strain, as demonstrated in the March model, furthermore enables the application of phyllosilicate pole figures in a strain determination in slate belts. Both applications are illustrated in this paper, in which the results are presented of a crystallographic fabric analysis of argillites in the southern domain of the lower Paleozoic Stavelot-Venn Massif (Belgium). In these argillites the development of a phyllosilicate preferred orientation is primarily defined by the low-grade metamorphism and the deformation history. The metamorphism, causing recrystallisation to be active during cleavage development, assures the development of a high degree of preferred orientation. On the other hand, the deformation history defines the type of phyllosilicate pole figure pattern. Based on the distinction of different pole figure patterns, a possible strain path for the argillites in the southern domain of the Stavelot-Venn Massif is proposed. An axially symmetric pole figure pattern indicates a Caledonian cleavage development in a pure flattening regime. The Variscan cleavage development, on the other hand, is characterised by an additional extensional component in the cleavage plane. If the primary phyllosilicate fabric, due to a pre-deformational compaction or a Caledonian cleavage development, underwent a complete reorientation caused by syntectonic recrystallisation, a typical orthorhombic pole figure pattern is formed. Otherwise a transition pole figure pattern develops, reflecting the superposition of the Variscan cleavage development on a pre-existing Caledonian cleavage fabric. The general deformation history of the southern domain of the Stavelot-Venn Massif differs substantially from that described for the northern domain. Contrary to the northern domain the southern domain seems to have undergone considerable Variscan deformation.

Analyzing skewed symmetries

Symmetry is pervasive in both man-made objects and nature. Since symmetries project to skew symmetries, finding axes of skew symmetry is an important vision task. This paper presents a linear time algorithm for finding the axes of skew symmetry, where the degree of symmetry is known. First, we present a review and critique of current methods for finding the axes of skew symmetry. Next, we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a “shear symmetry” and recovering the shear parameter of a reflexive symmetry. Using this approach, the authors derive a direct, non-heuristic moment-based technique for finding the axes of skew symmetry. For skew symmetric figures with degree of symmetry less than five we obtain a closed-form solution. The method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour's degree of symmetry. It is the first algorithm to find the axes of skew symmetry inO(n) time, where n is the number of contour points. The method is especially suited to industrial applications where the degree of symmetry is often knowna priori. Examples of the method are presented for both real and synthetic images, and an error analysis of the method is given.

Application of elliptic Fourier descriptors to symmetry detection under parallel projection

In this paper, the method of elliptic Fourier descriptors using arc length parameterization is applied to tackle the problem of detection and recovery of symmetry under parallel projection. A simple and fast iteration algorithm together with the invariants of symmetry provides sufficient information for the detection and recovery of symmetry under parallel projection. The proposed method has been extensively tested using symmetric figures under different parallel projections. Simulation results of the algorithm are presented. The extension of this method for planar object recognition under parallel projection is also addressed. >

Perfect colorings of multipatterns in the plane

In this paper we consider the problem of finding nontrivial perfect colorings of planar multipatterns. By a ‘multipattern’ we mean a symmetric planar figure, with symmetry group G, having several classes of motifs each transitive under the action of G. A perfect or symmetric coloring, then, is an assignment of colors to the motifs such that each symmetry operation of the group induces a unique permutation of the colors; we will here assume further that the action of G on the colors is transitive. If G is a wallpaper or frieze group, this is always possible and there is a number N( G), the coloring number of G, which is the minimum number (>1) of colors which suffice to color any multipattern with symmetry group G. In the case of finite groups, all multipatterns have nontrivial perfect colorings with the following exceptions: there are no nontrivial perfect colorings if some motif is fixed by all gϵG, or if G is the dihedral group dn with n=2 r , r⩾1 and motifs lie on all reflection axes. For wallpaper groups, 2⩽ N( G)⩽25. As a consequence it follows that every periodic k-isohedral tiling of the plane has a perfect coloring using at most 25 colors.

Detection of partial symmetry using correlation with rotated-reflected images

Symmetry is one of the important structural properties of a figure both in visual psychology and in computer vision. Symmetrical properties of planar two-dimensional figures are considered and a new method for the extraction of rotational symmetry and reflectional symmetry is presented. A figure is said to have symmetry if it is invariant with some congruent transformation which consists of translation, rotation and reflection. The approach is to obtain the congruent transformations which make the transformed image a good match with the original image. The directional correlation of edge features is used to evaluate how well the original and transformed images match. This method does not require any segmentation nor knowledge of the centroid position, and the symmetrical properties of partially symmetric figures can also be detected. The approach is described and this method is applied to synthetic and real images.

On finding the axes of skewed symmetry using the image normalization with moment

AbstractAmong the reconstruction methods for three‐dimensional information, methods are known for extracting the axes of skewed symmetry that place constraints on the orientation of the plane in space. Since skewed symmetry loses the symmetric nature for the most part, the many earlier methods for extracting axes of symmetry could not be directly applied to extracting axes of skewed symmetry. In addition, conventional methods for extracting the axes of skewed symmetry have the drawbacks of having long processing times and being difficult to apply to complex figures. In this paper, we propose a method that uses moments to perform a first‐order transform on a skew symmetric figure into a symmetric figure and then extracts the axes of symmetry. In this method, the problem is simplified by transforming a skew symmetric figure into a symmetric figure so that conventional methods for extracting the axes of symmetry can be applied. In addition, the evaluation of symmetry which uses the fact that the areas on both sides of an axis of symmetry are equal is adopted in the proposed extraction of the axes of symmetry. The features of this method are discussed by giving practical examples of extracting the axes of skewed symmetry.

Strain Relaxation During Growth Of Epitaxial Fe on Cu(O01)/MgO(001)

AbstractThe strain relaxation of sputter-deposited epitaxial Fe on Cu(001)/MgO(001) was observed in-situ for coverages of I to 200 equivalent monolayers of Fe. Grazing incidence x-ray scattering (GIXS) with synchrotron radiation allowed the precise determination of the in-plane strain in the Fe film. The highest observed elastic strain for the Fe was -10.3% which is in agreement with the lattice parameter mismatch between Fe and Cu for both (001)- and {211}-oriented growth. In-plane rocking curves revealed a bifurcation of the Fe(110) and Fe(220) peaks which is due to the rotation of islands to reduce strain energy. The angle of rotation of these islands was found to depend upon the amount of strain relaxation that had occurred in each island, in agreement with a simple theory for strain relaxation via the creation of a misfit dislocation network. The absence of Fe(200) intensity at small Fe thicknesses, coupled with out-of-plane symmetric and pole figure scans, suggest that Fe islands are tilted out of the plane of the sample about the Fe<110> axes by an angle consistent with Fe{211}-oriented growth. At larger thicknesses Fe(001) growth becomes dominant.

Ehud's Dagger: Patronage, Tyrannicide, and "Killing No Murder"

will begin with tyrannicidal counteremblem. In late essay, Michel Foucault characterized his life's work as a history of different modes by which, in our culture, human beings are made subjects (Dreyfus and Rabinow 208).1 Foucault gives us no more striking and influential example of this than opening pages of Discipline and Punish, which recount public execution of Robert-Fran;ois Damiens, who tried to assassinate Louis XV of France. Foucault quotes contemporary witnesses who describe how king's servants tore Damiens's flesh with pincers, burnt him with sulphur, poured boiling oil and molten lead, resin, and wax into his wounds, listened to his exclamations and confession, tied him to horses, severed his sinews, drew him, quartered him, and burnt him to ashes. The ritual execution of Damiens helps Foucault establish graphic contrast between one system of penal subjectification and another. The ancien regime punishes attack on body of king with an almost theatrical reproduction of crime in execution of guilty man, turning him into the symmetrical inverted figure of

Graphic precision: Controlling stimulus displays on IBM PC-compatible computers

Tachistoscopic presentation of stimuli on IBM PC-compatible computers is limited by a number of factors, including video retrace rates, screen scrolling, and the shape and density of picture elements. A method is presented for overcoming these difficulties through the use of enhanced graphic adapters or video graphic arrays. A C-language program demonstrates (1) synchronous scroll-free displays achieved by writing alternating images to “hidden” pages of video memory, (2) alternative techniques for erasing images, and (3) use of an empirically derived aspect ratio to produce symmetrical figures.

Method for computing homogeneous liquid-crystal conoscopic figures

A model is presented for computing the conoscopic figures produced by a uniformly oriented liquid crystal (LC) in a thin cell observed with a polarizing microscope. The method takes account of refraction and primary reflection at each interface within the cell but neglects multiple reflections. It is shown that the form of the isochromes in the figures is given qualitatively by the intersections of Bertin’s surfaces with the LC surface but that refraction also influences the form of the isochromes. Examples of calculated conoscopic figures are presented, including the symmetric flash figure and the optic-normal figure. The way in which these are altered by small changes in the optic-axis orientation is demonstrated. To complete the model, the polarizing effect of the microscope condenser and objective lens systems is estimated by calculating the Fresnel coefficients for model lens systems; the effect on the conoscopic figures is noted. Finally the director tilt in a 7-μm chiral smectic C LC cell is determined by comparing an experimentally measured figure with a set of calculated figures.

Circle as a symmetrical figure

Circle as a symmetrical figure