Bode, C., Helmy, M., & Bertamini, M. (2017). A cross-cultural comparison for preference for symmetry: comparing British and Egyptians non-experts..

The aesthetic appeal of symmetry has been noted and discussed by artists, historians and scientists. To what extent this appeal is universal is a difficult question to answer. From a theoretical perspective, cross-cultural comparisons are important, because similarities would support the universality of the response to symmetry. Some pioneering work has focussed on comparisons between Britain and Egypt (Soueif & Eysenck, 1971, 1972), including both experts and naive subjects. These studies confirmed some degree of universal agreement in preferences for simple abstract symmetry. We revisited this comparison after almost half a century. We compared preferences of naïve students in Egypt (n = 200) and Britain (n= 200) for 6 different classes of symmetry in novel, abstract stimuli. We used three different measurements of complexity: Gif ratio, Edge length and the average cell size (average blob size, ABS). The results support Soueif & Eysenck’s findings regarding preferences for reflectional and rotational symmetry, however they also throw new light on a greater preference for simplicity in Egyptian participants already noted by Soueif & Eysenck (1971)

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Testing Planarity of Geometric Automorphisms in Linear Time

It is a well-known result that testing a graph for planarity and, in the affirmative case, computing a planar embedding can be done in linear time. In this paper, we show that the same holds if additionally we require that the produced drawing be symmetric with respect to a given automorphism of the graph. This problem arises naturally in the area of automatic graph drawing, where symmetric and planar drawings are desired whenever possible

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented

Tracking Extended Objects in Noisy Point Clouds with Application in Telepresence Systems

We discuss theory and application of extended object tracking. This task is challenging as sensor noise prevents a correct association of the measurements to their sources on the object, the shape itself might be unknown a priori, and due to occlusion effects, only parts of the object are visible at a given time. We propose an approach to track the parameters of arbitrary objects, which provides new solutions to the above challenges, and marks a significant advance to the state of the art

Characterization of approximate plane symmetries for 3D fuzzy objects

International audienceWe are interested in finding and characterizing the symmetry planes of fuzzy objects in 3D space. We introduce first a fuzzy symmetry measure which defines an object symmetry degree with respect to a given plane. It is computed by measuring the similarity between the original object and its reflection. The choice of an appropriate measure of comparison is based on the desired properties. In a second part, a method for finding the best symmetry planes of fuzzy objects is proposed. We then apply these results to the representation of directional relationships

On Dispersion and Multipath Effects in Harmonic Radar Imaging Applications

In harmonic radar applications, it has been noticed that images produced using algorithms of conventional radar applications experience some defocusing effects of the electronic targets’ impulse response. This is typically explained by the dispersive transfer functions of the targets. In addition, it has been experimentally observed that objects with a linear transfer behavior do not contribute to the received signal of a harmonic radar measurement. However, some signal contributions based on a multipath propagation can overlay the desired signal, which leads to an undesired and unusual interference caused by the non-linear character of the electronic targets. In here, motivated by the analysis of measured harmonic radar data, the effects of both phenomena are investigated by theoretical derivations and simulation studies. By analyzing measurement data, we show that the dispersion effects are caused by the target, and not by the measurement system or the measurement geometry. To this end, a signal model is developed, with which it is possible to describe both effects, dispersion and multipath propagation. In addition, the discrepancy between classic radar imaging and harmonic radar is analyzed