Polygonal Complexes and Graphs for Crystallographic Groups

The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the classification of regular polygonal complexes, chiral polyhedra, and more generally, two-orbit polyhedra.Comment: 21 pages; In: Symmetry and Rigidity, (eds. R.Connelly, A.Ivic Weiss and W.Whiteley), Fields Institute Communications, to appea

Nongeometry, Duality Twists, and the Worldsheet

In this paper, we use orbifold methods to construct nongeometric backgrounds, and argue that they correspond to the spacetimes discussed in \cite{dh,wwf}. More precisely, we make explicit through several examples the connection between interpolating orbifolds and spacetime duality twists. We argue that generic nongeometric backgrounds arising from duality twists will not have simple orbifold constructions and then proceed to construct several examples which do have a consistent worldsheet description.Comment: v2-references added; v3-minor correction (eqn. 4.17

Traditional and new principles of perceptual grouping

Perceptual grouping refers to the process of determining which regions and parts of the visual scene belong together as parts of higher order perceptual units such as objects or patterns. In the early 20th century, Gestalt psychologists identified a set of classic grouping principles which specified how some image features lead to grouping between elements given that all other factors were held constant. Modern vision scientists have expanded this list to cover a wide range of image features but have also expanded the importance of learning and other non-image factors. Unlike early Gestalt accounts which were based largely on visual demonstrations, modern theories are often explicitly quantitative and involve detailed models of how various image features modulate grouping. Work has also been done to understand the rules by which different grouping principles integrate to form a final percept. This chapter gives an overview of the classic principles, modern developments in understanding them, and new principles and the evidence for them. There is also discussion of some of the larger theoretical issues about grouping such as at what stage of visual processing it occurs and what types of neural mechanisms may implement grouping principles

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

Oblique-wing supersonic aircraft

An aircraft including a single fuselage having a main wing and a horizontal stabilizer airfoil pivotally attached at their centers to the fuselage is described. The pivotal attachments allow the airfoils to be yawed relative to the fuselage for high speed flight, and to be positioned at right angles with respect to the fuselage during takeoff, landing, and low speed flight. The main wing and the horizontal stabilizer are upwardly curved from their center pivotal connections towards their ends to form curvilinear dihedrals

Opposition and Identicalness: Two Basic Components of Adults' Perception and Mental Representation of Symmetry

Symmetry is a salient aspect of biological and man-made objects, and has a central role in perceptual organization. Two studies investigate the role of opposition and identicalness in shaping adults’ naïve idea of “symmetry”. In study 1, both verbal descriptions of symmetry (either provided by the participants or selected from among alternatives presented by the experimenter) and configurations drawn as exemplars of symmetry were studied. In study 2, a pair comparison task was used. Both studies focus on configurations formed by two symmetrical shapes (i.e., between-objects symmetry). Three main results emerged. The explicit description of symmetry provided by participants generally referred to features relating to the relationship perceived between the two shapes and not to geometrical point-by-point transformations. Despite the fact that people tended to avoid references to opposition in their verbal definition of symmetry in study 1, the drawings that they did to represent their prototypical idea of symmetry manifested opposition as a basic component. This latter result was confirmed when the participants were asked to select the definition (in study 1) or the configuration (in study 2) that best fitted with their idea of symmetry. In conclusion, identicalness is an important component in people’s naïve idea of symmetry, but it does not suffice: opposition complements it

The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation

The visual system is sensitive to symmetries in the frontoparallel plane, and bilateral symmetry about a vertical axis has a particular salience. However, these symmetries represent only a subset of the symmetries realizable in three-dimensional space. The retinal image symmetries formed when viewing natural objects are typically the projections of three-dimensional objects—animals, for example—that have a symmetry in depth. To characterize human sensitivity to depth symmetry, experiments measured observers’ ability to discriminate stereo displays that were symmetrically distributed in depth and those that were asymmetrically distributed. Disparity values were distributed about one of four planes passing through the z-axis and differing in frontoparallel orientation. Asymmetrical patterns were generated by perturbing one of these disparities. Symmetrical-asymmetrical discrimination thresholds were lowest for symmetry about the vertical plane and highest for the horizontal plane. Thresholds for discriminating repetitions and non-repetitions of depth values did not differ across the four planes, whereas discriminations for depth gradients differed from both the symmetry and repetition cases. The heightened sensitivity to symmetry in depth about the vertical plane is a 3-D analog of 2-D mirror-image symmetry performance and could be its source