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Previous research indicated that most salient, real-world objects possess natural regularities that observers commonly assume in perceptual judgments of figural orientation and interpretation. Regularities include 3-dimensionality, bilateral symmetry, and the tendency for object tops to possess more salient information than bottoms. Thus, when observers interpret randomly shaped figures, they reliably impose volume, bilateral symmetry, and top and front orientation directions, even when figures are 2-dimensional and asymmetric. We confirmed generalizability for observers to assume these regularities with stimuli that vary in complexity, and we found evidence supporting another regularity, that of symmetry verticality (symmetry about a vertical axis). Findings support use of a family of perceptual heuristics corresponding to natural regularities that constrain stimulus indeterminacy and help guide judgment of object orientation and interpretation.

Phylogenetic analyses of asymmetry variation offer a powerful tool for exploring the interplay between ontogeny and evolution because (i) conspicuous asymmetries exist in many higher metazoans with widely varying modes of development, (ii) patterns of bilateral variation within species may identify genetically and environmentally triggered asymmetries, and (iii) asymmetries arising at different times during development may be more sensitive to internal cytoplasmic inhomogeneities compared to external environmental stimuli. Using four broadly comparable asymmetry states (symmetry, antisymmetry, dextral, and sinistral), and two stages at which asymmetry appears developmentally (larval and postlarval), I evaluated relations between ontogenetic and phylogenetic patterns of asymmetry variation. Among 140 inferred phylogenetic transitions between asymmetry states, recorded from 11 classes in five phyla, directional asymmetry (dextral or sinistral) evolved directly from symmetrical ancestors proportionally more frequently among larval asymmetries. In contrast, antisymmetry, either as an end state or as a transitional stage preceding directional asymmetry, was confined primarily to postlarval asymmetries. The ontogenetic origin of asymmetry thus significantly influences its subsequent evolution. Furthermore, because antisymmetry typically signals an environmentally triggered asymmetry, the phylogenetic transition from antisymmetry to directional asymmetry suggests that many cases of laterally fixed asymmetries evolved via genetic assimilation.

Descriptions are given of three kinds of symmetries encountered in studies of bacterial locomotion, and of the ways in which they are circumvented or broken. A bacterium swims at very low Reynolds number: it cannot propel itself using reciprocal motion (by moving through a sequence of shapes, first forward and then in reverse); cyclic motion is required. A common solution is rotation of a helical filament, either right- or left-handed. The flagellar rotary motor that drives each filament generates the same torque whether spinning clockwise or counterclockwise. This symmetry is broken by coupling to the filament. Finally, bacterial populations, grown in a nutrient medium from an inoculum placed at a single point, usually move outward in symmetric circular rings. Under certain conditions, the cells excrete a chemoattractant, and the rings break up into discrete aggregates that can display remarkable geometric order.

The biological realm has inherited symmetries from the physicochemical realm, but with the increasing complexity at higher phenomenological levels of life, some inherited symmetries are broken while novel symmetries appear. These symmetries are of two types, structural and operational. Biological novelties result from breaking operational symmetries. They are followed by acquisition of regularity and stability, in a recurrent process throughout complexity levels.

Is fluctuating asymmetry a powerful new tool for biologists or just an alluring new dance step? When studied with care, subtle deviations from symmetry offer a unique measure of developmental [...]

Cell-to-cell signalling mediates the regulation of left-right development in vertebrates. Ectopic expressions in embryos of the members of three significant peptide families, Wnt, Shn, and activin, lead to randomization of left-right asymmetries. The segmental signalling pathway in left-right development of chick embryos by Levin and associates is discussed.

A truncated icosahedron P has the proper symmetry group, icosahedral PSl(2, 5), which is a subgroup of the 660-element group PSl(2, 11) that has a 60-element conjugacy class M. M, which contains elements of order 11, has a model for P that expresses graph structure using group-based harmonic analysis. The 12 pentagons, which are the optimal commuting subsets of M, illustrate the theory.

Transdisciplinary programme explores the pervasive presence of symmetry violations. Transdisciplinary programme explores the pervasive presence of symmetry violations., Author Affiliations: Asymmetry symposium unites economists, physicists and artists Asymmetry -- seen here in the work of Bridget Riley -- could offer common ground between science and art. Credit: Dan [...]

The Robert G. Heft's, design of a union consisting of two interlocking grids destined to last even longer than the 48-star model is described. The discovery of the 51-star lattice design with the same rotational symmetry is been derived on the trial and error basis.

The embryo has the same set of molecules for the growth and maintenance of asymmetry of organs as diverse as those used in the development of insect wings, vertebrate limbs and the spinal cord. A study conducted on chicken embryos indicates that genes such as 'goosecoid' and FGF4 are symmetrically expressed in the node and the activin receptor IIb is more prominent on the right side of the node, whereas in the Sonic hedgehog, the receptor is found on the left side. However, these findings cannot be generalized, as mammals and zebrafish are exceptions.