scholarly journals Goodness of Regularity in Dot Patterns: Global Symmetry, Local Symmetry, and Their Interactions

Perception ◽  
10.1068/p5794 ◽  
2007 ◽  
Vol 36 (9) ◽  
pp. 1305-1319 ◽  
Author(s):  
Massimo Nucci ◽  
Johan Wagemans
Keyword(s):  
Mirror Symmetry ◽  
Local Symmetry ◽  
Detection Task ◽  
Global Symmetry ◽  
Different Types ◽  
Operational Models ◽  
Local Mirror Symmetry ◽  
Axes Of Symmetry ◽  
Global And Local ◽  
Short Presentation

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.

Local and global color symmetries of a symmetrical pattern

2019 ◽  
Vol 75 (5) ◽  
pp. 730-745
Author(s):  
Agatha Kristel Abila ◽  
Ma. Louise Antonette De Las Peñas ◽  
Eduard Taganap
Keyword(s):  
Symmetry Group ◽  
Local Symmetry ◽  
Global Symmetry ◽  
Color Symmetry ◽  
Usual Approach ◽  
Symmetrical Pattern ◽  
Symmetry Theory ◽  
Global Symmetry Group ◽  
Local Symmetries ◽  
Global And Local

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

The Internal Structure of a Rectangular Frame: Position, Orientation, and Direction

2015 ◽  
Vol 3 (1) ◽  
pp. 19-52 ◽  
Author(s):  
Stefano Guidi ◽  
Stephen E. Palmer
Keyword(s):  
Empirical Study ◽  
Goodness Of Fit ◽  
Reference Frames ◽  
Symmetry Axis ◽  
Local Symmetry ◽  
Aesthetic Response ◽  
Line Segments ◽  
Rectangular Frame ◽  
Axes Of Symmetry ◽  
Global And Local

Previous research has shown that the structure of a rectangular frame strongly influences perceived goodness-of-fit for a small circular probe positioned within it (Palmer and Guidi, 2011). The center is consistently rated as the best position, followed by positions along the global vertical, global horizontal, and local diagonal symmetry axes. Here we report how goodness-of-fit within a surrounding frame is influenced by the relation between with the orientational and directional structure of the probe and that of the frame. In Experiment 1, fit ratings of short line segments and small ovals (each with two symmetry axes) at 35 positions and four orientations within the frame revealed strong orientational effects, especially when the probe’s and frame’s axes of symmetry were aligned. Experiment 2 extended the paradigm using triangular probes (with a single symmetry axis) at 15 positions and eight pointing directions. The results showed high fit ratings when the probe was aligned with global and local symmetry axes of the frame, and directional increments when the probes pointed upward, rightward, and into the frame. Experiment 3 confirmed the upward, rightward, and inward directional effects of Experiment 2 using a more sensitive Two-Alternative Forced Choice (2AFC) task. Experiment 4 showed that orientational effects were more strongly driven by alignment with the rectangle’s sides than with gravitational or retinal reference frames, especially when the probe was near the sides and vertices of the frame. The relevance of these findings to the empirical study of aesthetic response to images within rectangular frames is discussed.

Mirror Symmetry Opposes Splitting of Chromatically Homogeneous Surfaces

Perception ◽  
10.1068/p3218 ◽  
2002 ◽  
Vol 31 (6) ◽  
pp. 693-709 ◽  
Author(s):  
Giulia Parovel ◽  
Stefano Vezzani
Keyword(s):  
Global Solution ◽  
Mirror Symmetry ◽  
Minimum Principle ◽  
Main Hypothesis ◽  
General Correlation ◽  
Local Factors ◽  
Single Figure ◽  
Axes Of Symmetry ◽  
Global And Local

Chromatically homogeneous surfaces can be seen as single figures but also as two or more overlapping figures. Local factors such as relatability have been proposed in order to explain perception of two or more figures (Kellman and Shipley, 1991 Cognitive Psychology23 141 – 221). However, even when these factors are at work, there are conditions favouring the perception of a single figure, which have not been explored so far. Here we propose that one such factor is the mirror symmetry of the surface. Three experiments were designed to test: (a) the main hypothesis, that mirror symmetry enhances perception of a single figure; (b) the role of orientation; (c) the effect of the number of axes of symmetry. The results show that (i) there is a good general correlation between mirror symmetry and perception of a single figure; (ii) vertical and horizontal axes of symmetry are the most effective; and (iii) the more axes of symmetry a surface has, the more likely is the perception of a single figure. These results suggest that mirror symmetry is an important factor in the perception of chromatically homogeneous displays. Some explanations are discussed, particularly one based on the rejection-of-coincidence principle [Rock, 1983 The Logic of Perception (Cambridge, MA: MIT Press)], and a version of the minimum principle in which the strength of the global solution depends on symmetry, whereas the strength of the splitting solution depends on the strength of local factors. In brief, global and local factors compete in determining the perceptual outcome in chromatically homogeneous surfaces.

The limits of strain and lattice parameter measurements by CBED

1989 ◽  
Vol 47 ◽  
pp. 518-519
Author(s):  
Hamish L. Fraser
Keyword(s):  
Electron Beam ◽  
Mirror Symmetry ◽  
Local Symmetry ◽  
Lattice Parameter ◽  
Growth Direction ◽  
Surface Relaxation ◽  
Strained Layer ◽  
Axis Parallel ◽  
Local Lattice ◽  
Strained Layer Superlattice

The topic of strain and lattice parameter measurements using CBED is discussed by reference to several examples. In this paper, only one of these examples is referenced because of the limitation of length. In this technique, scattering in the higher order Laue zones is used to determine local lattice parameters. Work (e.g. 1) has concentrated on a model strained-layer superlattice, namely Si/Gex-Si1-x. In bulk samples, the strain is expected to be tetragonal in nature with the unique axis parallel to [100], the growth direction. When CBED patterns are recorded from the alloy epi-layers, the symmetries exhibited by the patterns are not tetragonal, but are in fact distorted from this to lower symmetries. The spatial variation of the distortion close to a strained-layer interface has been assessed. This is most readily noted by consideration of Fig. 1(a-c), which show enlargements of CBED patterns for various locations and compositions of Ge. Thus, Fig. 1(a) was obtained with the electron beam positioned in the center of a 5Ge epilayer and the distortion is consistent with an orthorhombic distortion. When the beam is situated at about 150 nm from the interface, the same part of the CBED pattern is shown in Fig. 1(b); clearly, the symmetry exhibited by the mirror planes in Fig. 1 is broken. Finally, when the electron beam is positioned in the center of a 10Ge epilayer, the CBED pattern yields the result shown in Fig. 1(c). In this case, the break in the mirror symmetry is independent of distance form the heterointerface, as might be expected from the increase in the mismatch between 5 and 10%Ge, i.e. 0.2 to 0.4%, respectively. From computer simulation, Fig.2, the apparent monocline distortion corresponding to the 5Ge epilayer is quantified as a100 = 0.5443 nm, a010 = 0.5429 nm and a001 = 0.5440 nm (all ± 0.0001 nm), and α = β = 90°, γ = 89.96 ± 0.02°. These local symmetry changes are most likely due to surface relaxation phenomena.

SYMMETRY GEOMETRY BY PAIRINGS

2018 ◽  
Vol 106 (03) ◽  
pp. 342-360 ◽  
Author(s):  
G. CHIASELOTTI ◽  
T. GENTILE ◽  
F. INFUSINO
Keyword(s):  
Closure Operator ◽  
Local Symmetry ◽  
Global Symmetry ◽  
Symmetry Relation ◽  
Basic Tool ◽  
Mathematical Structures ◽  
Finite Case ◽  
Set Systems ◽  
Power Set ◽  
Abstract Simplicial Complex

In this paper, we introduce asymmetry geometryfor all those mathematical structures which can be characterized by means of a generalization (which we call pairing) of a finite rectangular table. In more detail, let$\unicode[STIX]{x1D6FA}$be a given set. Apairing$\mathfrak{P}$on$\unicode[STIX]{x1D6FA}$is a triple$\mathfrak{P}:=(U,F,\unicode[STIX]{x1D6EC})$, where$U$and$\unicode[STIX]{x1D6EC}$are nonempty sets and$F:U\times \unicode[STIX]{x1D6FA}\rightarrow \unicode[STIX]{x1D6EC}$is a map having domain$U\times \unicode[STIX]{x1D6FA}$and codomain$\unicode[STIX]{x1D6EC}$. Through this notion, we introduce a local symmetry relation on$U$and a global symmetry relation on the power set${\mathcal{P}}(\unicode[STIX]{x1D6FA})$. Based on these two relations, we establish the basic properties of our symmetry geometry induced by$\mathfrak{P}$. The basic tool of our study is a closure operator$M_{\mathfrak{P}}$, by means of which (in the finite case) we can represent any closure operator. We relate the study of such a closure operator to several types of others set operators and set systems which refine the notion of an abstract simplicial complex.

scholarly journals Self-organizing Systems in the Light of the Arrows of Orderedness, Symmetry, and Entropy

1970 ◽  
Vol 2 (2) ◽  
pp. 63-73
Author(s):  
György Darvas
Keyword(s):  
Second Law Of Thermodynamics ◽  
Local Symmetry ◽  
Evolution Of The Universe ◽  
Global Evolution ◽  
New Material ◽  
New Interpretation ◽  
The One ◽  
Global And Local ◽  
The Universe ◽  
Matter Energy

The paper makes an attempt to resolve two conceptual mingling: (a) the mingling of the two interpretations of the concept of orderedness applied in statistical thermodynamics and in symmetrology, and (b) the mingling of two interpretations of evolution applied in global and local processes. In conclusion, it formulates a new interpretation on the relation of the emergence of new material qualities in selforganizing processes on the one hand, and the evolution of the universe, on the other. The process of evolution is a sequence of emergence of new material qualities by self-organization processes, which happen in negligible small segments of the universe. Although thermodynamics looks at the universe as a closed (isolated) system, this holds for its outside boundaries only, while the universe has many subsystems inside, which are not isolated (closed), since they are in a permanent exchange of matter, energy, etc. with their environment (with the rest of the universe) through their open boundaries. Any ";;emergence";; takes place, i.e., all new qualities come into being just in these small open segments of the universe. The conditions to apply the second law of thermodynamics are not present here. Therefore, global evolution of the universe is the consequence of local symmetry decreases, local decreases of orderedness, and possible local decreases of entropy.

scholarly journals [N′-(4-Decyloxy-2-oxidobenzylidene)-3-hydroxy-2-naphthohydrazidato-κ3N,O,O′]dimethyltin(IV): crystal structure and Hirshfeld surface analysis

2017 ◽  
Vol 73 (3) ◽  
pp. 390-396
Author(s):  
Siti Nadiah Binti Mohd Rosely ◽  
Rusnah Syahila Duali Hussen ◽  
See Mun Lee ◽  
Nathan R. Halcovitch ◽  
Mukesh M. Jotani ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Mirror Symmetry ◽  
Chelate Ring ◽  
Hirshfeld Surface ◽  
Methyl Groups ◽  
Coordination Geometry ◽  
Trigonal Bipyramidal ◽  
First Approximation ◽  
Benzene Rings ◽  
Local Mirror Symmetry

The title diorganotin compound, [Sn(CH3)2(C28H32N2O4)], features a distorted SnC2NO2coordination geometry almost intermediate between ideal trigonal–bipyramidal and square-pyramidal. The dianionic Schiff base ligand coordinates in a tridentate fashionviatwo alkoxide O and hydrazinyl N atoms; an intramolecular hydroxy-O—H...N(hydrazinyl) hydrogen bond is noted. The alkoxy chain has an all-transconformation, and to the first approximation, the molecule has local mirror symmetry relating the two Sn-bound methyl groups. Supramolecular layers sustained by imine-C—H...O(hydroxy), π–π [between decyloxy-substituted benzene rings with an inter-centroid separation of 3.7724 (13) Å], C—H...π(arene) and C—H...π(chelate ring) interactions are formed in the crystal; layers stack along thecaxis with no directional interactions between them. The presence of C—H...π(chelate ring) interactions in the crystal is clearly evident from an analysis of the calculated Hirshfeld surface.

scholarly journals Assessing Landscape Ecological Risk Induced by Land-Use/Cover Change in a County in China: A GIS- and Landscape-Metric-Based Approach

2020 ◽  
Vol 12 (21) ◽  
pp. 9037 ◽  
Author(s):  
Jianxiao Liu ◽  
Meilian Wang ◽  
Linchuan Yang
Keyword(s):  
Land Use ◽  
Ecological Risk ◽  
Research Area ◽  
Ecological Vulnerability ◽  
Different Types ◽  
Landscape Ecological ◽  
Global And Local ◽  
The Relationship ◽  
Regional Land ◽  
Resolution Data

Landscape ecological risk assessment (LERA) evaluates different types of potential environmental impacts and their cumulative effects, thereby providing policy insights for sustainable regional land-use and ecosystem management. In a departure from existing literature that heavily relies on low-resolution land-use data for LERA at provincial or municipal scales, this study applies high-resolution land-use data to a relatively small research area (county). In addition, this study modifies the evaluation units of LERA from equal-sized grids to watersheds and refines the ecological vulnerability weight on the basis of finer-resolution data. The main findings are summarized as follows: (1) In 2011–2013, nearly 866 ha of land use in Xiapu County changed; moreover, the construction land, which was mainly concentrated in Songgang Street and Xinan Town, increased the most (340 ha). (2) Landscape ecological risk (LER) was roughly maintained, and areas of high ecological risk were mainly concentrated along the coast. (3) The spatial distribution of LER maintained a relatively aggregated pattern, with no trend toward more aggregated or more dispersed change. This study further discusses the relationship between local LER and land-use change and how to balance global and local LER in planning practices.

scholarly journals Lost in Learning: Hypertext Navigational Efficiency Measures Are Valid for Predicting Learning in Virtual Reality Educational Games

2020 ◽  
Vol 11 ◽  
Author(s):  
Chris Ferguson ◽  
Herre van Oostendorp
Keyword(s):  
Virtual Reality ◽  
Educational Games ◽  
Educational Game ◽  
Knowledge Test ◽  
Efficiency Measures ◽  
Unobtrusive Measure ◽  
Different Types ◽  
Cognitive Overload ◽  
Two Measures ◽  
Global And Local

The lostness measure, an implicit and unobtrusive measure originally designed for assessing the usability of hypertext systems, could be useful in Virtual Reality (VR) games where players need to find information to complete a task. VR locomotion systems with node-based movement mimic actions for exploration and browsing found in hypertext systems. For that reason, hypertext usability measures, such as “lostness” can be used to identify how disoriented a player is when completing tasks in an educational game by examining steps made by the player. An evaluation of two different lostness measures, global and local lostness, based on two different types of tasks, is described in a VR educational game using 13 college students between 14 and 18 years old in a first study and extended using 12 extra participants in a second study. Multiple Linear Regression analyses showed, in both studies, that local lostness, and not global lostness, had a significant effect on a post-game knowledge test. Therefore, we argued that local lostness was able to predict how well-participants would perform on a post-game knowledge test indicating how well they learned from the game. In-game experience aspects (engagement, cognitive interest, and presence) were also evaluated and, interestingly, it was also found that participants learned less when they felt more present in the game. We believe these two measures relate to cognitive overload, which is known to have an adverse effect on learning. Further research should investigate the lostness measure for use in an online adaptive game system and design the game system in such a way that the risk of cognitive overload is minimized when learning, resulting in higher retention of information.

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