Tilt aftereffects generated by bilaterally symmetrical patterns

Tilt aftereffects were generated by bilaterally symmetrical dot patterns. Both expansion and contraction effects, similar in size and magnitude to effects usually reported with luminance contours, were observed after adaptation to symmetrical patterns tilted 15 deg or 75 deg respectively from a vertically oriented test. Large effects were found when both adapting and test stimuli were symmetrical patterns while smaller effects were found when the adapting stimulus was symmetrical and test stimulus was a grating. A third experiment, which manipulated the number of dots near the axis line, confirmed the above findings; expansion and contraction effects were observed again. The results of these experiments suggest that the neural mechanism underlying the perception of luminance contours may be linked to the mechanism for the detection of symmetry.     

Symmetry types, systems and their multiplicity in the structure of adenovirus capsid. II. Rotational facet groups of five-, three- and two-fold symmetry axes

The icosahedral adenovirus capsid has three rotational symmetry axes of different types. The six five-fold, ten three-fold and the fifteen two-fold axes have two superficial points each, altogether 62. The axes determine the number and location of the identical rotational facet groups and that during the different rotational phases which other regular facets and with what multiplicity shall be covered by them. The number of rotational facets of the five-, three- and two-fold rotational symmetry axes is 4, 6.66 and 10, respectively. In all the three cases, there are two kinds of possible arrangements of the facets. During the rotation--when the facets of the facet group placed on one by one to the neighbouring identical facet groups--at the five-fold axes, the facets of the rotational facet group get into cover position 12 times with all the 20 regular capsid facets, 20 times at the three-fold axes, and 30 times at the two-fold axes in a way that a different facet combination (facet hit) falls to every facet, and the original symmetry is not disturbed. After all, this means 240, 400 and 600 facet combinations, i.e. multiplicity in case of five-, three- and two-fold symmetry axes respectively, and these numbers correspond with that of the theoretically possible variations. The same results can be calculated by multiplying the number of real rotations of the capsid bringing the body into itself, i.e. the number 60 with the number of facets contributing to the five-, three- and two-fold rotational phases. The other way of the determination of multiplicity takes into account that all the facet groups of the capsid rotate simultaneously during all the rotational phases, and this multiplies the number of multiplicity with the number of the rotational types five-, three- and two-fold which result in one and the same multiplicity number in the case of five-, three- and two-fold symmetry, alike 1200. Perpendicular to the five-fold symmetry axes with the line of intersection drawn horizontally in the middle along the 6 geodetic ribbon like motifs a regular decagonal intersection forms and the capsid can be cut into two equal parts, in which the polypeptides show a 72 degree rotation from each other, but with a proper rotation the polypeptides get into a congruent position, which means 300 or 600 specific facet combinations. The capsid similar to the icosahedron has also 15 virtual mirror planes which divide the capsid into two, identically arranged halves, forming six right angle triangles on each facet, altogether 120 smaller rectangular so-called Mobius-triangles on the surface. In the three-fold symmetry axis of the facets, these triangles in two separate groups of three can be rotated symmetrically with 120 degrees according to the orientation of the polypeptide subunits in a way that the hexon and other polypeptides too nearly cover each other. Consequently, the adenovirus capsid is a symmetrically arranged body in which several various symmetry types and symmetry systems can be found and their structural symmetry elements exist simultaneously and covering each other. The icosahedral symmetry types and systems are valid and functional simultaneously and in parallel with great multiplicity, but the existence of more than 1500 structural elements in several depth levels, their order of location and distribution make the symmetry of the capsid richer and more complex.     

Testing the Accuracy of Different A-Axis Types for Measuring the Orientation of Bones in the Archaeological and Paleontological Record

Orientation of archaeological and paleontological materials plays a prominent role in the interpretation of site formation processes. Allochthony and authochthony are frequently assumed from orientation patterns or lack thereof. Although it is still debated to what extent orientation of items can be produced in original depositional contexts, the recent use of GIS tools to measure orientations has highlighted several ways of reproducing A-axes with which to address these taphonomic issues. In the present study, the three most relevant A-axis types are compared to test their accuracy in reproducing water current direction. Although results may be similar in specific bone shapes, differences are important in other shapes. As known in engineering working with wind and fluid mechanics (developing shape optimization), longitudinal symmetrical axes (LSA) are the one that best orient structures against or in the same direction of wind and water. The present work shows that this is also the case for bones (regardless of shape), since LSA produce the most accurate estimates of flow direction. This has important consequences for the interpretation of orientation patterns at sites, since this type of axis is still not properly reproduced by GIS available tools.     

Matching the orientation of dot patterns with real, interpolated, and extrapolated lines

The perception of the orientation of random-dot patterns was studied using four different matching tasks. Homogeneous, elongated patterns and patterns containing Moiré effects were used. One of the tasks implied linear extrapolation and two others implied linear interpolation of the matching line. The fourth task was identical with those used in previous studies by the authors on this topic. Systematic deviations from the axes of orientation of the patterns were observed for the latter task when compared with the former ones. When a short matching line, implying linear extrapolation, was used performance by subjects tended to be more inaccurate than in the other matching tasks. The linear interpolation tasks, in which the matching line was determined by either two collinear distant short lines or by two distant dots, provided more accurate and stable performance than the other two tasks. The results are discussed from the point of view of global orientation perception derived from an image function of the stimuli.     

A REEVALUATION OF THE ZOSTEROPHYLLOPHYTINA WITH COMMENTS ON THE ORIGIN OF LYCOPODS

The primary paleobotanical literature pertaining to Zosterophyllophytina (a now extinct group of Devonian vascular plants) was reexamined for evidence concerning the activity of the apex of fertile shoots as it might be revealed by the presence or absence of terminally located sporangia (terminate or nonterminate axes, respectively). The symmetry of sporangial arrangement (radial or bilateral), the presence or absence of enations, circinate axial tips, and the shape of the vascular strand were also recorded. We found terminate axes usually are (but not invariably) associated with radial symmetry and nonterminate axes are typically bilateral in symmetry. Other morphological features are consistent with this observation, e.g., enations, circinate tips, and (when preserved) elliptic vascular strands are found in association with bilateral symmetry and nonterminate axes. We hypothesize that there are two distinct patterns of fertile axial growth within the Zosterophyllophytina. Nonetheless, all taxa currently assigned to the zosterophyllophytes share a reniform or globose sporangial shape and a distal line of dehiscence. Accordingly, we view Zosterophyllophytina as a monophyletic group of plants, whose members show two distinct patterns of growth in their fertile axes. We speculate that lycopods arose from an early zosterophyllophytelike group characterized by nonterminate, radially symmetrical fertile axes. We speculate that zosterophyllophytes with terminate fertile axes and those with nonterminate, bilaterally symmetrical fertile axes were phylogenetic deadends.     

Interocular orientation disparity and the stereoscopic perception of slanted surfaces

The orientation threshold for two-dimensional filtered noise stimuli was estimated using forced-choice procedures with both dioptic and dichoptic viewing. In the dioptic case the two patterns were co-rotated. In the dichoptic case the stimuli were counter-rotated to produce an orientation disparity, which yields a percept of slant about the horizontal axis orthogonal to the cyclopean line of sight. Dioptic thresholds increased with the orientation bandwidth of the stimuli. In contrast, dichoptic thresholds were essentially constant across a wide range of conditions. In all cases, dichoptic orientation acuity was much finer than conventional estimates. In a second experiment, the dichoptic threshold was estimated for patterns superimposed on a depth pedestal. Acuity was affected significantly by the presence of the pedestal, and was an inverse function of pedestal amplitude. The results suggest that stereoscopic slant caused by dichoptic counter-rotation arises because of neural processing of the overall pattern of disparities of position produced by counter-rotation, rather than specialised encoding of orientation disparity.     

Symmetry types, systems and their multiplicity in the structure of adenovirus capsid. I. Symmetry networks and general symmetry motifs

Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino-acids--are in symmetrical location. Every kind of polypeptide forms a separately also symmetrical network in the capsid distributed according to their functions in the inner and outer side and the inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four (GOF) according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each GOF orient toward the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the GOFs: the hexons surround either a polypeptide IX or a polypeptide IlIa. The two versions of GOFs on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the antisymmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an antisymmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest neighbouring facets. In the facets, the polypeptide subunits of polypeptide IX centered GOF hexons have identical counter-clockwise orientation but the orientation of the neighbouring facets is always opposite compared to each other. On the five-fold symmetry axis, any facet can be "turned on" to the adjacent facet or "rotated" to all the others and will take the symmetry and orientation of the facet it got turned on or rotated to. Thus, every facet together with the polypeptides attached to it shows a twenty-fold symmetry and multiplicity. An other type of symmetry and multiplicity in the capsid is that perpendicular to the 6 five-fold rotation axes run a geodetic (equatorial) ribbon like motif (superfieces) altogether six made up of 10 x 10 triangular facets and bent ten-times with an angle of 36 degrees. A triangular facet participates in forming three ribbon-like motifs, which intersect with each other on the given facet, but the same three motifs intersect repeatedly only on the antisymmetrically located facet.     

Coding of stimulus movement parameters in cat visual system

The principal component analysis of matrices composed of spike numbers generated by visual neurons of cats in response to motion of simple and complex stimuli revealed vector encoding. Responses of detectors of moving dot direction and detectors of oblique line orientation are encoded independently in V1 and V2 cortices by excitation of two cardinal neurons. Each pair of these neurons generates sine and cosine functions. Responses of detectors in the association cortex selective to specific orientation of moving stripes depend on the activity of four cardinal neurons which sum up the excitation incoming from the direction and orientation channels.     

Flower Symmetry Preferences in Honeybees and their Crab Spider Predators

Flowers exhibit symmetrical patterns, and innate preferences for symmetry in pollinators like honeybees are documented. Most previous studies of symmetry preferences in honeybees, Apis mellifera, tested levels of asymmetry using artificial flowers or stimuli. Here we investigated the effect of flower asymmetry on flower preferences of honeybees in a novel approach using real flowers, incorporating their spectral properties and how the receivers process the visual signals. Importantly, we also tested the response of an ‘eavesdropping’ predator, the crab spider Thomisus spectabilis, that also utilizes the same flower to prey on honeybees. Flowers (Chrysanthemum frutescens) were manipulated to contain asymmetrical and symmetrical patterns, excluding olfactory cues. Both crab spiders and honeybees exhibited a significant preference for symmetrical flowers. Moreover, honeybees exhibited a significant preference for radial symmetry over bilateral symmetry, but no corresponding effect was recorded in crab spiders. Further analyses demonstrated that flower reflectance and orientation of the axis of symmetry did not affect crab spider decisions. Field observations on T. spectabilis revealed that the natural variation in C. frutescens symmetry had no effect on the choice of crab spiders. This indicates that spiders and honeybees may use other flower characteristics, for example, olfactory cues, together with flower symmetry, to make their foraging decisions.     

Does assignment of orientation to dot patterns reveal optimization processes in the visual system?

Sixty subjects were tested to assign orientation to ten dot patterns differing in their overall form and the number of dots in the pattern. The patterns were presented in four different positions in the visual field and their orientation was estimated in two ways. It was demonstrated that the assignment of orientation did not depend on the position of the pattern in the visual field as well as on the method of estimation used. A quantitative measure for the elongation of a dot pattern is proposed which correlates with the degree of ambiguity in orientation estimation. The greater the elongation the smaller the standard deviation of the estimates given. The distributions of the estimates for the ten patterns were analyzed. It was shown that they can be presented as superpositions of two or more groups of normally distributed estimates determined by some salient characteristics of the stimuli. Data are discussed from the point of view that assignment of orientation to dot patterns reveals the existence of optimization mechanisms in human brain that extract perceptual invariants from external stimulation.     

Line Orientation Adaptation: Local or Global?

Prolonged exposure to an oriented line shifts the perceived orientation of a subsequently observed line in the opposite direction, a phenomenon known as the tilt aftereffect (TAE). Here we consider whether the TAE for line stimuli is mediated by a mechanism that integrates the local parts of the line into a single global entity prior to the site of adaptation, or the result of the sum of local TAEs acting separately on the parts of the line. To test between these two alternatives we used the fact the TAE transfers almost completely across luminance contrast polarity [1]. We measured the TAE using adaptor and test lines that (1) either alternated in luminance polarity or were of a single polarity, and (2) either alternated in local orientation or were of a single orientation. We reasoned that if the TAE was agnostic to luminance polarity and was parts-based, we should obtain large TAEs using alternating-polarity adaptors with single-polarity tests. However we found that (i) TAEs using one-alternating-polarity adaptors with all-white tests were relatively small, increased slightly for two-alternating-polarity adaptors, and were largest with all-white or all-black adaptors. (ii) however TAEs were relatively large when the test was one-alternating polarity, irrespective of the adaptor type. (iii) The results with orientation closely mirrored those obtained with polarity with the difference that the TAE transfer across orthogonal orientations was weak. Taken together, our results demonstrate that the TAE for lines is mediated by a global shape mechanism that integrates the parts of lines into whole prior to the site of orientation adaptation. The asymmetry in the magnitude of TAE depending on whether the alternating-polarity lines was the adaptor or test can be explained by an imbalance in the population of neurons sensitive to 1^st-and 2^nd-order lines, with the 2^nd-order lines being encoded by a subset of the mechanisms sensitive to 1^st-order lines.     

Symmetrical decorations enhance the attractiveness of faces and abstract designs

In humans and several other species, face and body symmetry have been found to enhance physical attractiveness. A proposed explanation is that symmetry is a phenotypic indicator of biological fitness. Throughout the world, symmetrical designs also are a common feature in face and body painting and the decorative arts. The implication is that symmetrical designs might provide an additional way to enhance physical attractiveness. To find out, we conducted three experiments, two with human faces and one with abstract or nonrepresentational designs. In Experiments 1 and 2, we showed undergraduate students photographs of pairs of faces and instructed them to choose the more attractive face in each pair. The photographs were of physically symmetrical and asymmetrical faces (as indexed by facial features) that had been decorated with either symmetrical or asymmetrical designs of the kind used in many preindustrial societies. As indexed by the number of times they were chosen, symmetrical faces were judged to be more attractive than asymmetrical faces; adding asymmetrical designs to symmetrical faces decreased their attractiveness; and adding symmetrical designs to asymmetrical faces increased their attractiveness. In Experiment 3, undergraduates made similar choices from pairs of abstract designs taken from several cultures and modified in shape, coloration, and orientation of design features. Symmetrical designs again were judged to be more attractive, with shape and coloration playing the more important roles. We interpret the results as suggesting that the same mechanisms underlying the judgment of physical attractiveness also underlie cultural practices of face painting and abstract art.     

Symmetry perception by poultry chicks and its implications for three-dimensional object recognition

Bilateral symmetry is visually salient to diverse animals including birds, but whereas experimental studies typically use bilaterally symmetrical two-dimensional patterns that are viewed approximately fronto-parallel; in nature, animals observe three-dimensional objects from all angles. Many animals and plant structures have a plane of bilateral symmetry. Here, we first (experiment I) give evidence that young poultry chicks readily generalize bilateral symmetry as a feature of two-dimensional patterns in fronto-parallel view. We then test the ability of chicks to recognize symmetry in images that would be produced by the transformed view produced by a 40° horizontal combined with a 20° vertical rotation of a pattern on a spherical surface. Experiment II gives evidence that chicks trained to distinguish symmetrical from asymmetrical patterns treat rotated views of symmetrical 'objects' as symmetrical. Experiment III gives evidence that chicks trained to discriminate rotated views of symmetrical 'objects' from asymmetrical patterns generalize to novel symmetrical objects either in fronto-parallel or rotated view. These findings emphasize the importance of bilateral symmetry for three-dimensional object recognition and raise questions about the underlying mechanisms of symmetry perception.     

Analysis of extracellular potentials using an IBM PC

1. A system has been developed for using IBM PC-compatible computers in combination with a Grafitek Data Logging Interface to record spike trains on magentic discs for later analysis. 2. The times and amplitudes of spikes detected on two input channels are recorded, together with a third channel containing information on computer-generated stimuli and keyboard-activated event markers. In excess of 50,000 spikes can be recorded with a computer having 640 k of Random Access Memory. 3. The recorded spike trains can be reconstructed on the computer monitor and keyboard-controlled window discriminators can be used to select the spikes for analysis by amplitude. 4. The same recorded data can be analysed to produce displays of spike count against time, amplitude histograms, inter-spike interval histograms, peri-stimulus time histograms(PSTH), raster displays and auto- and cross-correlations between activity on the two channels. Each spike is identified by number, allowing easy location of the start and finish of the section of data to be analysed, and the PSTH, raster and correlation analyses allow pretriggering to investigate event occurring before stimulation. 5. The axes of the displays histograms can be adjusted to produce optimum displays, and hard copy can be produced on dot matrix printers or digital plotters. 6. Quantitative analysis enables comparison between different recordings and treatments.     

Visual discrimination of radial cues by the honeybee (Apis mellifera)

This is a systematic study of the discrimination of black radially symmetrical patterns presented on a white vertical background and subtending 45 degrees or 50 degrees at the point of choice in a Y-maze apparatus. Before discrimination can occur, the ability to fixate is promoted by any radial pattern irrespective of the number of symmetry axes. A ring of spots can also stabilize the eye before the positions of the spots are discriminated.Cues for discrimination are of two main types. First, with fixed patterns of sectors or spots, the cue is the location of an area of black relative to the fixation point, and the particular number of axes is less important than the size of the individual areas. Secondly, evidence is presented for a family of filters with large fields and coarse tuning that detect patterns of radially symmetrical edges. These filters become more evident when the patterns are made of thin black radial bars or when they are rotated at random during the training. An angular shift of one radial pattern relative to the other, or a difference between numbers of bars, is best discriminated when one of the patterns but not the other has angles of 30 degrees, 60 degrees, or 120 degrees between radial edges, and least when the angles are 90 degrees. Baffles in the apparatus make the bees pause and fixate so that discrimination is improved. When targets are rotated during the learning process, radial cues for discriminations must be presented as edges, not as spots or areas. Besides detecting and fixating flowers, this system could be useful to estimate the perfection of their symmetry.     

Determination of 3D spinal kinematics without defining a local vertebral coordinate system

In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7° in a range of misalignments up to 10° between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.     

On visual orientation of dot patterns

Two-dimensional normally distributed random dot patterns were used in two experiments on visual orientation estimation. In the first experiment the patterns differed in their sample correlation and in dot number. In the second one the number of dots was maintained constant but the patterns were generated as a superposition of two normally distributed orthogonal sets composed of different number of dots. In both experiments the estimated orientation depended on stimuli correlation-with increasing correlation the estimated orientation gets closer to the orientation of the least square distance axis of the pattern. Even at very low unsignificant correlations there still remained a hint about stimulus orientation which was not estimated at random. Equalizing consecutively the number of dots in the two orthogonal dot patterns during the second experiment did not result in chance performance either. The bimodal angular distributions of the obtained responses permitted to approach the problem of orientation ambiguity. The results are discussed in terms of optimization processes taking place in the visual system.     

Quaternary structure of apoferritin: the rotation function at 9 A resolution

The rotation function has been calculated for apoferritin using data at 9 Å resolution obtained from cubic crystals, space group F432, and compared with rotation functions of possible alternative model structures consisting of (a) 24 subunits at the vertices of a snub-cube (octahedral symmetry) and (b) 20 subunits at the vertices of a pentagonal dodecahedron (icosahedral symmetry). The apoferritin rotation function, like that of the 24 subunit model, had large peaks only on the crystallographic rotation axes. The 20 subunit model gave peaks on non-crystallographic axes, which were not observed with apoferritin. It is concluded that apoferritin molecules consist of 24 subunits arranged in 432 (octahedral) symmetry as suggested by the space group.     

The perception of a dotted line in noise: a model of good continuation and some experimental results

A formal model is proposed, describing how the perceptual interpretation of dot figures is guided by the Gestalt rule of good continuation. The algorithm will be restricted to figures with a collinear dot array (line) embedded in a background of randomly placed dots. The model, CODE-2, is an elaboration of the model, CODE-1, of grouping dots on the basis of the Gestalt rule of (relative) proximity, and consists of the introduction of non-circular symmetric gaussian distribution functions for the representation of the orientation dependent strength of interaction between collinear dots. Supra-threshold contours of the function, resulting from a superposition on each dot of the gaussian functions, are assumed to predict the perceptual grouping of the dots. A quantitative measure for the perceptual salience of dotted lines was defined as the contrast between the internal coherence of the line dots, and their interference with the noise dots. For 20 stimuli the CODE-2 grouping of the dots is reported, together with the results of a line-in-noise latency experiment. There was a significant correlation between the predicted saliences and the experimental results. The results support the usefulness of representing good continuation between collinear dots by non-circular symmetric gaussian distribution functions.     

Electron cryo-microscopy and image reconstruction of adeno-associated virus type 2 empty capsids

Adeno-associated virus type 2 empty capsids are composed of three proteins, VP1, VP2 and VP3, which have relative molecular masses of 87, 72 and 62 kDa, respectively, and differ in their N-terminal amino acid sequences. They have a likely molar ratio of 1:1:8 and occupy symmetrical equivalent positions in an icosahedrally arranged protein shell. We have investigated empty capsids of adeno-associated virus type 2 by electron cryo-microscopy and icosahedral image reconstruction. The three-dimensional map at 1.05 nm resolution showed sets of three elongated spikes surrounding the three-fold symmetry axes and narrow empty channels at the five-fold axes. The inside of the capsid superimposed with the previously determined structure of the canine parvovirus (Q. Xie and M.S. Chapman, 1996, J. Mol. Biol., 264, 497–520), whereas the outer surface showed clear discrepancies. Globular structures at the inner surface of the capsid at the two-fold symmetry axes were identified as possible positions for the N-terminal extensions of VP1 and VP2.