Symmetry Of Pattern Research Articles

Geometric References of Roman Mosaics in North Africa

This paper deals with the geometric analysis of the Roman mosaics found in the domūs of the archaeological areas of Volubilis, in Morocco, and Bulla Regia, in Tunisia. It analyzes the expressions of mosaic art which in the Roman Empire, between the second and fourth centuries A.D., attained a particular geometric decorative refinement. The tessellation of the mosaics of Volubilis and Bulla Regia is just an example of a cultural universe that for centuries has been a testimony to the lifestyles and myths of the Roman Empire and that today, if appropriately exploited, could contribute to enhance the knowledge and the identity of the Mediterranean heritage. The research proposes a reading of the mosaic apparatus through the study of the constitutive geometric elements. This leads to an analysis useful for the classification of figures and symmetry patterns, and understanding of their meanings. The methodology adopted is that of disassembly and reassembly of areas of mosaic tiling, creating a dialogue between the two-dimensional geometric elements of the flooring and the architectural context in which they are inserted.

Substrate mediated interaction between pairs of keratocytes: Multipole traction force models describe their migratory behavior.

A series of traction force microscopy experiments involving pairs of keratocytes migrating on compliant substrates were analyzed. We observed several instances where keratocytes that are about to collide turn before they touch. We term this phenomenon collision avoidance behavior and we propose that the turning is caused by the substrate mediated elastic interactions between the cells. A multipole analysis of the cell traction reveals that the left-right symmetry of the keratocyte traction pattern is broken during collision avoidance events. The analysis further shows that the cell migration direction reorients before the principal traction dipoles as the cells turn. Linear elasticity theory is used to derive the cell-cell interaction energy between pairs of keratocytes. The traction force applied by each cell is modeled as a two points (dipole) or three points (tripod) force model. We show that both models predict that cells that are about to collide in a head-on manner will turn before touching. The tripod model is further able to account for the quadrupole components of the traction force profile that we observed experimentally. Also, the tripod model proposes a mechanism that may explain why cells tend to scatter with a finite angle after a collision avoidance event. A relationship between the scattering angle and the traction force quadrupole moment is also established. Dynamical simulations of migrating model cells are further used to explain the emergence of other cell pair trajectories that we observed experimentally.

The representation of symmetry in multi-voxel response patterns and functional connectivity throughout the ventral visual stream

Several computational models explain how symmetry might be detected and represented in the human brain. However, while there is an abundance of psychophysical studies on symmetry detection and several neural studies showing where and when symmetry is detected in the brain, important questions remain about how this detection happens and how symmetric patterns are represented. We studied the representation of (vertical) symmetry in regions of the ventral visual stream, using multi-voxel pattern analyses (MVPA) and functional connectivity analyses. Our results suggest that neural representations gradually change throughout the ventral visual stream, from very similar part-based representations for symmetrical and asymmetrical stimuli in V1 and V2, over increasingly different representations for symmetrical and asymmetrical stimuli which are nevertheless still part-based in both V3 and V4, to a more holistic representation for symmetrical compared to asymmetrical stimuli in high-level LOC. This change in representations is accompanied by increased communication between left and right retinotopic areas, evidenced by higher interhemispheric functional connectivity during symmetry perception in areas V2 and V4.

Mesoamerican Antecedents of Sikyatki-Style Geometric Patterns on Textiles Depicted in Murals from the American Southwest

This paper uses plane pattern symmetries to describe the structural arrangement of motifs in Sikyatki-style patterns on textiles depicted in fourteenth and fifteenth century AD kiva murals from Awat'ovi and Kawaika'a in Arizona and Pottery Mound in New Mexico. The analysis reveals that these textiles have pattern structures in common with designs on textiles, ceramic artifacts, and architectural decorations in the Postclassic Mixteca-Puebla style. These shared patterns and pattern structures were introduced into the American Southwest woven on fabric structures of textiles brought north from Mesoamerica via trade and migration routes along the Mexican West Coast and through the Sierra Madre.

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann–Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was 53.67 years with a standard deviation of 8.20 years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.

Pupil segmentation in the light-field camera and its relation to 3D object positions and the reconstructed depth of field.

A ray-trace simulation of the light-field camera is used to calculate point source responses as a function of 3D source positions. Each point source location yields a unique and well-determined segmented-pupil pattern in the lenslet array's focal plane, with lateral object offsets changing the pattern's location and symmetry, and defocus distances altering the pattern's diameter. Segmented-pupil images can thus be used to infer point sources' 3D locations. Numerical simulations show that the centroids and widths of segmented pupil images can be used to deduce lateral image positions to the size of a detector pixel, and image defocus to the accuracy of the lenslet focal length. In sparse-source cases, such as, e.g., fluorescence microscopy or particle tracking, 3D point-source locations can thus be accurately determined from the observed point source response patterns. The degree of pupil segmentation also directly constrains the ability to refocus light-field images-for image defocus distances large enough that the number of pupil segments exceeds the number of pixels within a "whole" pupil behind a single lenslet, the image can no longer be brought to focus numerically, thus defining the light-field camera's depth of field. This constraint implies a depth of field larger than the usual imaging depth of focus by a factor of the number of detector pixels per lenslet, consistent with the general expectation.

A local measure of symmetry and orientation for individual spikes of grid cells.

Grid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.

Three‐dimensional circular patch antenna under TM 02 mode with improved impedance matching

A circular patch antenna under TM 02 mode with improved impedance matching is proposed by adopting 3D architecture. It is known that the TM 02 mode of circular patch can generate omnidirectional radiation, but its input resistance reaches maximum at centre point. In this context, impedance matching is difficult to be achieved and the feeding probe is often supposed to be placed a distance away from the centre, inevitably destroying the symmetry of radiation pattern. Without introducing pins or slots, a direct strategy is here employed where the circular patch is folded to form a concave at its centre. It is found that the input resistance can be effectively reduced with increasing depth of concave since the described concave serves as vertical electric wall in cavity and weakens the electric field in the region between centre and ground. By using electroplate technology based on plastics, a 3D antenna prototype is fabricated and measured to validate the proposed methodology.

Gene duplication and relaxation from selective constraints of GCYC genes correlated with various floral symmetry patterns in Asiatic Gesneriaceae tribe Trichosporeae.

Floral bilateral symmetry is one of the most important acquisitions in flower shape evolution in angiosperms. Members of Gesneriaceae possess predominantly zygomorphic flowers yet natural reversal to actinomorphy have independently evolved multiple times. The development of floral bilateral symmetry relies greatly on the gene CYCLOIDEA (CYC). Our reconstructed GCYC phylogeny indicated at least five GCYC duplication events occurred over the evolutionary history of Gesneriaceae. However, the patterns of GCYC expression following the duplications and the role of natural selection on GCYC copies in relation to floral symmetry remained largely unstudied. The Asiatic tribe Trichosporeae contains most reversals to actinomorphy. We thus investigated shifts in GCYC gene expression among selected zygomorphic species (Hemiboea bicornuta and Lysionotus pauciflorus) and species with reversals to actinomorphy (Conandron ramondioides) by RT-PCR. In the actinomorphic C. ramondioides, none of the three copies of GCYC was found expressed in petals implying that the reversal was a loss-of-function event. On the other hand, both zygomorphic species retained one GCYC1 copy that was expressed in the dorsal petals but each species utilized a different copy (GCYC1C for H. bicornuta and GCYC1D for L. pauciflorus). Together with previously published data, it appeared that GCYC1C and GCYC1D copies diversified their expression in a distinct species-specific pattern. To detect whether the selection signal (ω) changed before and after the duplication of GCYC1 in Asiatic Trichosporeae, we reconstructed a GCYC phylogeny using maximum likelihood and Bayesian inference algorithms and examined selection signals using PAML. The PAML analysis detected relaxation from selection right after the GCYC1 duplication (ωpre-duplication = 0.2819, ωpost-duplication = 0.3985) among Asiatic Trichosporeae species. We propose that the selection relaxation after the GCYC1 duplication created an "evolutionary window of flexibility" in which multiple copies were retained with randomly diverged roles for dorsal-specific expressions in association with floral symmetry changes.

Symmetry in the diffraction of beams carrying orbital angular momentum

Diffraction of orbital-angular-momentum--carrying Laguerre-Gauss vortex (LGV) beams by $N$-fold rotationally symmetric regular polygons is studied analytically and experimentally. The structure, symmetry, and dependence of the diffraction pattern on the angular momentum index of the LGV beam and the number of sides in the polygon are systematically investigated, and features and trends are identified. The evolution of the diffraction pattern and its symmetry with the aperture position relative to the waist is also studied, leading to a generalized Friedel's law for diffraction of LGV beams.

Feedback of mantle metasomatism on olivine micro–fabric and seismic properties of the deep lithosphere

The interaction of hydrous fluids and melts with dry rocks of the lithospheric mantle inevitably modifies their viscoelastic and chemical properties due to the formation of compositionally distinct secondary phases. In addition, melt percolation and the associated metasomatic alteration of mantle rocks may also facilitate modification of the pre–existing rock texture and olivine crystallographic preferred orientation (CPO) and thus seismic properties. Here we explore the relationship between mantle metasomatism, deformation and seismic anisotropy using subduction–related mantle xenoliths from the Penghu Islands, western Taiwan. The investigated xenoliths have equilibrated at upper lithospheric mantle conditions (879 °C to 1127 °C) based on pyroxene geothermometry and show distinct variations in clinopyroxene chemical composition, texture and olivine CPO allowing for the classification of two distinct groups. Group 1 xenoliths contain rare earth element (REE) depleted clinopyroxene, show a porphyroclastic texture and olivine grains are mostly characterized by [100]–axial pattern symmetries. In contrast, REE-enriched clinopyroxene from Group 2 xenoliths occur in a fine–grained equigranular texture and coexisting olivine frequently displays [010]–axial pattern symmetries. The clinopyroxene compositions are indicative of cryptic and modal to stealth metasomatic alteration of Group 1 and Group 2 xenoliths, respectively. Furthermore, the observed olivine [100]–axial pattern of Group 1 xenoliths reflects deformation by dislocation creep at high temperature, low pressure and dry conditions, whereas olivine [010]–axial patterns of Group 2 xenoliths imply activation of olivine [001] glide planes along preferentially wet (010) grain boundaries. This correlation indicates that the variation in olivine CPO symmetry from [100]– to [010]–axial pattern in Penghu xenoliths results from deformation and intra-crystalline recovery by subgrain rotation during metasomatic alteration induced by melt percolation. The microstructural observations and olivine CPO combined with petrological and geochemical data suggest that Group 1 xenoliths preserve microstructural and chemical characteristics of an old, probably Proterozoic lithosphere, while Group 2 xenoliths record localized Miocene deformation associated with wall–rock heating and metasomatism related to melt circulation. Furthermore, the observed transition of olivine CPO from [100]–axial pattern to [010]–axial pattern by deformation in the presence of variable melt fractions and associated metasomatic alteration can be inferred to modify the physical properties of mantle rocks.

A Novel 2D—Grid of Scroll Chaotic Attractor Generated by CNN

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x = y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array ( 1 × 3 ) cells. The paper concerns on the design and implementation of 2 × 2 and 3 × 3 2 D -grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

Ion induced ferromagnetism combined with self-assembly for large area magnetic modulation of thin films.

A highly versatile and scalable path to obtain buried magnetic nanostructures within alloy thin films, while maintaining a flat topography, is described. A magnetic pattern of nanoscale periodicity is generated over ∼cm2 areas by employing a B2 → A2 structural transition in the prototype Fe60Al40 thin alloy films. The phase transition was induced in the confined regions via ion-irradiation through self-assembled nanosphere masks. In this way, large area patterns of a hexagonal symmetry of ferromagnetic nanostructures embedded within a paramagnetic Fe60Al40 thin film are realized. The depth and lateral distribution of the induced magnetization was investigated by magnetometry and microscopy methods. Magnetic contrast imaging as well as simulations shows that the obtained magnetic structures are well defined, with the magnetic behavior tunable via the mask geometry.

CrossFit athletes exhibit high symmetry of fundamental movement patterns. A cross-sectional study

CrossFit athletes exhibit high symmetry of fundamental movement patterns. A cross-sectional study

Design of a Novel Compact Slotted Cavity With Shaped Beam for High Power Microwave Feed Antenna Using Asymmetric High Order Mode

In order to achieve a shaped beam on a compact aperture and reduce the cost and the volume, a conformal slotted cavity as a feed antenna for high-power microwave using the asymmetric high-order mode is investigated. The proposed antenna working in a high-order mode has merits on reducing the complexity of a power network and the volume of a mode converter. The alternate arrangement of the slot array is taken into account, and the asymmetric high-order mode TE 430 is selected to improve the symmetry of far-field pattern at the E-plane. A novel design of wide slot with the horn-cavity etched on the top surface of the upper cavity achieves the uniform aperture field and mitigates the maximum electric field enhancement, and calculated results verify that the proposed antenna is capable of high-power handling capability (above 1.29 GW in vacuum). The conformal slot array is introduced to obtain a shaped beam, which helps to illuminate reflect array with shaped aperture efficiently. The simulation and measured results show that the feed antenna achieves a low-profile structure of 2.4λ 0 × 2.8λ 0 × 0.8λ 0 , the 10-dB gain beamwidth of E-plane is 56.6° at the operating frequency of 9.1 GHz, the maximum difference of the gain, and the 10-dB beamwidth angle between the two sides of main beam is no more than 1 dB and 1°, respectively.

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

The classifications approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions are critically reviewed and their relative performance qualitatively evaluated. The information theory based approach of the author utilizes digital images and turns out to be the only one that allows for fully objective classifications of the crystallographic symmetries, i.e. Bravais lattice type, Laue class, and plane symmetry group, of noisy real-world images. His information theory based crystallographic symmetry classifications utilize geometric bias-corrected sums of squared residuals, i.e. pertinent first order information, and enable the most meaningful crystallographic averaging in the spatial frequency domain, which suppresses generalized noise much more effectively than traditional Fourier filtering. Taking account of the fact that it is fundamentally unsound to assign an abstract mathematical concept such as a single symmetry type, class, or group with 100 % certainty to a more or less 2D periodic record of a noisy real-world imaging experiment that involved a real-world sample, the information theory based approach to crystallographic symmetry classifications delivers probabilistic classifications. Recent applications of deep convolutional neural networks to classifications of crystallographic translation symmetries in 2D and crystals in three dimensions are discussed as these machines deliver probabilistic classifications by non-analytical means.

Mericarp morphology of the tribe Selineae (Apiaceae, Apioideae) and its taxonomic implications in Korea

Mericarp morphology of 24 taxa belonging to nine genera of the tribe Selineae (Family: Apiaceae) in Korea was studied by Scanning Electron Microscopy. UPGMA and NMDS analyses were performed based on 12 morphological characters. The mericarp surface characters like mericarp shape, rib number and shape, surface pattern, surface appendages and mericarp symmetry proved useful in distinguishing the genera of the tribe Selineae.

Visual search pattern during free viewing of horizontally flipped images in patients with unilateral spatial neglect

Eye tracking is an effective tool for identifying behavioural aspects of unilateral spatial neglect (USN), which is a common neurological syndrome that develops after a right hemisphere lesion. Here, we attempted to elucidate how the neglect symptom affects the symmetry of the gaze pattern, by performing an analysis of gaze distribution during the free viewing of a pair of horizontally flipped images. Based on their Behavioural Inattention Test (BIT) scores, 41 patients with right-hemisphere damage were classified into those with USN (n = 27) and those without USN (right hemisphere damaged - RHD; n = 14). Eye movement was recorded while the patients viewed six pairs of horizontally flipped images on a computer display. A pair of flipped images has both similar and consistent elements, as well as a reversed spatial location of objects (right-left). We calculated the gaze distribution, extent of gaze shift, total gaze distance, and gaze velocity in each direction. Our results demonstrated a significantly larger rightward gaze shift in the USN group, which showed a significant correlation with the BIT score. More importantly, the extent of gaze shift and total gaze distance were similarly modulated by the contents of the displayed images in both the USN and RHD groups. Our findings suggest that analyses of gaze distribution during the free viewing of a pair of horizontally flipped images have the potential to precisely reveal neglect behaviour, and our results provide important implications for rehabilitation.

Geometric morphometrics of nested symmetries unravels hierarchical inter- and intra-individual variation in biological shapes

Symmetry is a pervasive feature of organismal shape and the focus of a large body of research in Biology. Here, we consider complex patterns of symmetry where a phenotype exhibits a hierarchically structured combination of symmetries. We extend the Procrustes ANOVA for the analysis of nested symmetries and the decomposition of the overall morphological variation into components of symmetry (among-individual variation) and asymmetry (directional and fluctuating asymmetry). We illustrate its use with the Aristotle’s lantern, the masticatory apparatus of ‘regular’ sea urchins, a complex organ displaying bilateral symmetry nested within five-fold rotational symmetry. Our results highlight the importance of characterising the full symmetry of a structure with nested symmetries. Higher order rotational symmetry appears strongly constrained and developmentally stable compared to lower level bilateral symmetry. This contrast between higher and lower levels of asymmetry is discussed in relation to the spatial pattern of the lantern morphogenesis. This extended framework is applicable to any biological object exhibiting nested symmetries, regardless of their type (e.g., bilateral, rotational, translational). Such cases are extremely widespread in animals and plants, from arthropod segmentation to angiosperm inflorescence and corolla shape. The method therefore widens the research scope on developmental instability, canalization, developmental modularity and morphological integration.

Generating symmetric graphs

Symmetry in graphs which describe the underlying topology of networked dynamical systems plays an essential role in the emergence of clusters of synchrony. Many real networked systems have a very large number of symmetries. Often one wants to test new results on large sets of random graphs that are representative of the real networks of interest. Unfortunately, existing graph generating algorithms will seldom produce graphs with any symmetry and much less ones with desired symmetry patterns. Here, we present an algorithm that is able to generate graphs with any desired symmetry pattern. The algorithm can be coupled with other graph generating algorithms to tune the final graph's properties of interest such as the degree distribution.