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Journal articles on the topic 'Quantitative symmetry'

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Author: Grafiati

Published: 10 March 2023

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1

HUEBNER, KAI, DANIEL WESTHOFF, and JIANWEI ZHANG. "OPTIMIZED QUANTITATIVE BILATERAL SYMMETRY DETECTION." International Journal of Information Acquisition 02, no. 03 (September 2005): 241–49. http://dx.doi.org/10.1142/s021987890500060x.

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In [Westhoff et al., 2005], we proposed a novel method to determine illumination-invariant features in images. The quantitative bilateral symmetry of a given scene is computed using dynamic programming before applying the resulting symmetry image and feature vector signatures to an omnidirectional motion tracking task. Compared to other approaches to symmetry detection in computer vision, the results of our novel algorithm describe symmetry in terms of an absolute region instead of a relative degree. In this paper, we describe further optimizations and details of the proposed Dynamic Programming Symmetry feature detection algorithm (DPS algorithm).

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2

Tamir, Abraham. "Quantitative Analysis of Face Symmetry." Journal of Craniofacial Surgery 26, no. 4 (June 2015): 1268–69. http://dx.doi.org/10.1097/scs.0000000000001610.

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3

Tripathi, Amit, and V. K. Gairola. "Fold symmetry—a quantitative description." Journal of Structural Geology 21, no. 7 (July 1999): 719–27. http://dx.doi.org/10.1016/s0191-8141(99)00066-8.

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4

Chen, Yangyang, Yi Zhao, and Xinyu Han. "Characterization of Symmetry of Complex Networks." Symmetry 11, no. 5 (May 20, 2019): 692. http://dx.doi.org/10.3390/sym11050692.

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Recently, symmetry in complex network structures has attracted some research interest. One of the fascinating problems is to give measures of the extent to which the network is symmetric. In this paper, based on the natural action of the automorphism group Aut ( Γ ) of Γ on the vertex set V of a given network Γ = Γ ( V , E ) , we propose three indexes for the characterization of the global symmetry of complex networks. Using these indexes, one can get a quantitative characterization of how symmetric a network is and can compare the symmetry property of different networks. Moreover, we compare these indexes to some existing ones in the literature and apply these indexes to real-world networks, concluding that real-world networks are far from vertex symmetric ones.

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5

Kim, Kyou-Hyun, and Jian-Min Zuo. "Quantitative symmetry determination and symmetry mapping using convergent beam electron diffraction technique." Microscopy and Microanalysis 21, S3 (August 2015): 821–22. http://dx.doi.org/10.1017/s1431927615004900.

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6

Daunoraviciene, Kristina, Jurgita Ziziene, Agne Ovcinikova, Rasa Kizlaitiene, and Julius Griskevicius. "Quantitative body symmetry assessment during neurological examination." Technology and Health Care 28, no. 5 (September 21, 2020): 573–84. http://dx.doi.org/10.3233/thc-208003.

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BACKGROUND: A lack of movement coordination characterized by the undershoot or overshoot of the intended location with the hand, arm, or leg is often found in individuals with multiple sclerosis (MS). Standardized as Finger-to-Nose (FNT) and The Heel-to-Shin (HST) tests are the most frequently used tests for qualitative examination of upper and lower body coordination. Inertial sensors facilitate in performing quantitative motion analysis and by estimating body symmetry more accurately assess coordination lesion and imbalance. OBJECTIVES: To assess the body symmetry of upper and lower limbs quantitatively, and to find the best body symmetry indices to discriminate MS from healthy individuals (CO). METHODS: 28 MS patients and 23 CO participated in the study. Spatiotemporal parameters obtained from six Inertial Measurement Units (IMUs) were placed on the upper and lower extremities during FNT and HST tests. All data were analyzed using statistical methods in MATLAB. RESULTS: Asymmetry indices of temporal parameters showed a significant increase in upper body and lower body asymmetry of MS compared to CO. However, CO have a greater kinematic asymmetry compared to MS. CONCLUSION: Temporal parameters are the most sensitive to body asymmetry evaluation. However, range of motion is completely inappropriate if it is calculated for one movement cycle.

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Li, David Xinzheyang, Maha S. Ead, Kajsa K. Duke, Jacob L. Jaremko, and Lindsey Westover. "Quantitative analysis of regional specific pelvic symmetry." Medical & Biological Engineering & Computing 59, no. 2 (January 16, 2021): 369–81. http://dx.doi.org/10.1007/s11517-020-02296-5.

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Vincent, R., and T. D. Walsh. "Quantitative assessment of symmetry in CBED patterns." Ultramicroscopy 70, no. 1-2 (December 1997): 83–94. http://dx.doi.org/10.1016/s0304-3991(97)00080-6.

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9

Hsiao, Yu-Ching, Chen-Jung Chang, and Jing-Jing Fang. "Quantitative Asymmetry Assessment between Virtual and Mixed Reality Planning for Orthognathic Surgery—A Retrospective Study." Symmetry 13, no. 9 (September 2, 2021): 1614. http://dx.doi.org/10.3390/sym13091614.

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Orthognathic surgical planning compromises three clinical needs: occlusal balancing, symmetry, and harmony, which may result in multiple outcomes. Facial symmetry is the ultimate goal for patients and practitioners. Pure virtual planning and mixed reality planning were two innovative technologies in clinical practices compared to conventional model surgery used for decades. We proposed quantitative asymmetry assessment methods in both mandibular contour (in 2D) and a midface and mandible relationship in 3D. A computerized optimal symmetry plane, being the median plane, was applied in both planning methods. In the 3D asymmetry assessment between two planning methods, the deviation angle and deviation distance between midface and mandible were within 2° and 1.5 mm, respectively. There was no significant difference, except the symmetry index of the anterior deviation angle between the virtual and mixed reality planning in the 3D asymmetry assessment. In the mandible contour assessment, there was no significant difference between the virtual and mixed reality planning in asymmetry assessment in the frontal and frontal downward inclined views. Quantitative outcomes in 3D asymmetry indices showed that mixed reality planning was slightly more symmetric than virtual planning, with the opposite in 2D contouring.

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10

Petitjean, Michel. "On the root mean square quantitative chirality and quantitative symmetry measures." Journal of Mathematical Physics 40, no. 9 (September 1999): 4587–95. http://dx.doi.org/10.1063/1.532988.

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11

Bauerly, Michael P., and Yili Liu. "Development and Validation of a Symmetry Metric for Interface Aesthetics." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 49, no. 5 (September 2005): 681–85. http://dx.doi.org/10.1177/154193120504900510.

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This article describes the experimental investigation of the effects of symmetry on judgments of interface aesthetics. Thirty compositions were developed in order to validate symmetry quantification algorithms with subjective aesthetic ratings. The same compositions were used in two experiments, one using basic black-and-white images, and the other using web pages. The images were rated by 16 subjects in each experiment using the ratio-scale magnitude estimation method against a benchmark image. Subjects also established an ordered list of the images according to their aesthetic appeal using the balanced incomplete block (BIB) ranking method. The results show that subjects are adept at rating symmetry about both horizontal and vertical axes and their ratings closely match the quantification algorithm. Additionally, the relation between the dominant symmetry value and aesthetic appeal shows that subjects preferred symmetric images over non-symmetric images for the black-and-white imagery. The development and validation of the symmetry metric is an important step towards developing quantitative evaluation metrics for interface aesthetics evaluation and design.

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12

Gazit-Rappaport, T. "Quantitative evaluation of lip symmetry in functional asymmetry." European Journal of Orthodontics 25, no. 5 (October 1, 2003): 443–50. http://dx.doi.org/10.1093/ejo/25.5.443.

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13

Gazit-Rappaport, T., E. Gazit, and M. Weinreb. "Quantitative evaluation of lip symmetry in skeletal asymmetry." European Journal of Orthodontics 29, no. 4 (June 7, 2007): 345–49. http://dx.doi.org/10.1093/ejo/cjm022.

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14

Yogev-Einot, Dina, and David Avnir. "Pressure and temperature effects on the degree of symmetry and chirality of the molecular building blocks of low quartz." Acta Crystallographica Section B Structural Science 60, no. 2 (March 18, 2004): 163–73. http://dx.doi.org/10.1107/s0108768104003647.

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We establish quantitative correlations between pressure and temperature (PT) changes, and the degree of symmetry and of chirality of the main molecular building blocks of low quartz that these PT changes induce. The distortion from ideal tetrahedral symmetry, from helicity (deviation from C 2 symmetry), and the level of chirality are evaluated quantitatively using the continuous-symmetry and chirality-measures approach. These measures are global and reflect all changes in bond angles and bond lengths. The specific molecular building blocks analyzed are the SiO4 elementary building block (which is found to be chiral!), the Si(OSi)4 unit, the second-shell SiSi4 tetrahedron [composed of the five Si atoms of Si(OSi)4] and the four-tetrahedra helix fragment, —O(SiO3)4—. The temperature and pressure effects on symmetry and chirality were found to mirror each other in all building blocks. By employing this quantitative approach to symmetry and chirality we were able to combine the pressure effects and temperature effects into a unified picture. Furthermore, the global nature of the symmetry measure allows the comparison of the behavior of isostructural materials such as germania and quartz. For these crystals it has been shown that the symmetry/chirality behavior of germania at low pressures is a predictor for the behavior of these structural properties in quartz at higher pressures. Finally, given that the rigid SiO4 unit undergoes only minor structural changes, it has been a useful observation that the symmetry/chirality of the small SiSi4 tetrahedron is a very sensitive probe for the symmetry and chirality changes in quartz as a whole.

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15

Saimoto, S., R. G. Kamat, P. Clarke, and P. van Houte. "A Quantitative Method to Examine Through Thickness Texture Variation." Textures and Microstructures 21, no. 2-3 (January 1, 1993): 109–20. http://dx.doi.org/10.1155/tsm.21.109.

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Through thickness texture variation is a reality in commercial sheet stock. However, methods to quantitatively evaluate this variation and its effects are not readily available. In this study, it was shown that a hot rolled commercial aluminium sheet manifests variation in rolling texture components which can be detected by traverse scan of the peak intensity across the through thickness using tapered specimens. Moreover, this asymmetry can be correlated to the intensity asymmetry observed in pole figures. A quantitative analysis is possible if the ODF is generated using monoclinic symmetry with the transverse direction as the diad axis instead of the conventional orthorhombic symmetry.

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16

Николаев, В. В., К. А. Иванов, К. М. Морозов, and А. В. Белоновский. "Метод матриц рассеяния для расчета спонтанной излучательной рекомбинации в структурах с цилиндрической симметрией." Физика и техника полупроводников 54, no. 7 (2020): 654. http://dx.doi.org/10.21883/ftp.2020.07.49506.9336.

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Abstract A method is developed for analyzing spontaneous-emission modification in cylindrically symmetric structures. A matrix method is developed for cylindrical structures. General expressions for the radiative-recombination rate are derived for an emitter placed at any point on the structure. Quantitative indicators for estimating radiative-recombination enhancement and suppression are determined; they can be considered as modal Purcell factors. An expression for the total Purcell factor is derived for an emission direction perpendicular to the symmetry axes of the medium; as well as an expression for the integral (total) Purcell factor for the emitter at the symmetry axis.

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17

Magnanini, Rolando, and Giorgio Poggesi. "Interpolating estimates with applications to some quantitative symmetry results." Mathematics in Engineering 5, no. 1 (2022): 1–21. http://dx.doi.org/10.3934/mine.2023002.

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<abstract><p>We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $ L^p $ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimates hold for a general class of domains, including, e.g., Lipschitz domains. All the constants involved can be explicitly computed. As an application, we show how to use these estimates to obtain stability for Alexandrov's Soap Bubble Theorem and Serrin's overdetermined boundary value problem. The new approach results in several novelties and benefits for these problems.</p></abstract>

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18

Rafelski, Susanne, Jacob Schroder, Carolina Torrealba, Melanie Mueller, Xiaolei Su, Monica Guo, Wallace Marshall, et al. "Quantitative Test for Mirror Symmetry Relationship between Sister Cells." Biophysical Journal 98, no. 3 (January 2010): 430a. http://dx.doi.org/10.1016/j.bpj.2009.12.2329.

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19

Bhatia, P. K., and H. C. Taneja. "On quantitative-qualitative measure of inaccuracy and reversible symmetry." Information Sciences 67, no. 3 (January 15, 1993): 277–82. http://dx.doi.org/10.1016/0020-0255(93)90076-x.

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20

Woodard, Katerina, and Jiri Neustupa. "Geometric Morphometrics of Bilateral Asymmetry in Eunotia bilunaris (Eunotiales, Bacillariophyceae) as a Tool for the Quantitative Assessment of Teratogenic Deviations in Frustule Shapes." Symmetry 14, no. 1 (December 30, 2021): 42. http://dx.doi.org/10.3390/sym14010042.

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A number of pennate diatom genera typically have teratogenic deformations of their siliceous frustules due to the effects of environmental stress, such as high concentrations of heavy metals and low pH. However, the quantitative assessment of these deformations has rarely been applied. One species in which aberrations have frequently been reported is Eunotia bilunaris, which typically has bilaterally symmetric frustules with dorso-ventral differentiation. In this study, we aimed to illustrate the geometric morphometric analysis of symmetry as a tool for assessing the severity of teratogenic deformations. These were quantified by Procrustes superimposition of equidistant points placed along the valvar outlines in pairs of configurations based on their bilateral reflection symmetry. The shape deformations were mostly confined to central parts of the ventral outlines and were captured both by the symmetric and asymmetric subspaces of the variation. The amount of bilateral asymmetry in individual cells was negatively related to frustule size via the allometric power law relationship, illustrating that asymmetry increased in the asexual diminution series. The presented analysis provides a framework for the quantitative assessment of frustule deformations in eunotioid diatoms that can be used for the comparative scoring of teratogenic deviations among cells, populations, or species.

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21

Byng, J. W., N. F. Boyd, L. Little, G. Lockwood, E. Fishell, R. A. Jong, and M. J. Yaffe. "Symmetry of projection in the quantitative analysis of mammographic images." European Journal of Cancer Prevention 5, no. 5 (October 1996): 319–27. http://dx.doi.org/10.1097/00008469-199610000-00003.

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22

Saragusti, I., I. Sharon, O. Katzenelson, and D. Avnir. "Quantitative Analysis of the Symmetry of Artefacts: Lower Paleolithic Handaxes." Journal of Archaeological Science 25, no. 8 (August 1998): 817–25. http://dx.doi.org/10.1006/jasc.1997.0265.

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23

DAHIYA, HARLEEN, and NEETIKA SHARMA. "STRANGENESS AND CHIRAL SYMMETRY BREAKING." Modern Physics Letters A 26, no. 04 (February 10, 2011): 279–88. http://dx.doi.org/10.1142/s0217732311034785.

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The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model (χCQM). The role of hidden strangeness component has been investigated for the scalar matrix elements of the nucleon with an emphasis on the meson–nucleon sigma terms. The χCQM is able to give a qualitative and quantitative description of the "quark sea" generation through chiral symmetry breaking. The significant contribution of the strangeness is consistent with the recent available experimental observations.

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24

Lychagina, Tatiana, and Dmitry Nikolayev. "Quantitative comparison of measured crystallographic texture." Journal of Applied Crystallography 49, no. 4 (July 27, 2016): 1290–99. http://dx.doi.org/10.1107/s1600576716009730.

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A new approach for the determination of a quantitative measure to compare pole figures for different specimens is presented. The suggested approach is based on the Kolmogorov–Smirnov test. A new quantitative similarity measure between the textures of different specimens is suggested. This measure is verified by means of numerical models for both cubic and hexagonal crystalline symmetry, and it is applied to real experimental data for railway wheel steel. A comparison between the existing RP value and the introduced KSP value is presented to illustrate the specific character of the latter.

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25

DIJKSTRA, HENK A., and M. JEROEN MOLEMAKER. "Symmetry breaking and overturning oscillations in thermohaline-driven flows." Journal of Fluid Mechanics 331 (January 25, 1997): 169–98. http://dx.doi.org/10.1017/s0022112096003874.

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The bifurcation structure of thermohaline-driven flows is studied within one of the simplest zonally averaged models which captures thermohaline transport: a Boussinesq model of surface-forced thermohaline flow in a two-dimensional rectangular basin. Under mixed boundary conditions, i.e. prescribed surface temperature and fresh-water flux, it is shown that symmetry breaking originates from a codimension-two singularity which arises through the intersection of the paths of two symmetry-breaking pitchfork bifurcations. The physical mechanism of symmetry breaking of both the thermally and salinity dominated symmetric solution is described in detail from the perturbation structures near bifurcation. Limit cycles with an oscillation period in the order of the overturning time scale arise through Hopf bifurcations on the branches of asymmetric steady solutions. The physical mechanism of oscillation is described in terms of the most unstable mode just at the Hopf bifurcation. The occurrence of these oscillations is quite sensitive to the shape of the prescribed fresh-water flux. Symmetry breaking still occurs when, instead of a fixed temperature, a Newtonian cooling condition is prescribed at the surface. There is only quantitative sensitivity, i.e. the positions of the bifurcation points shift with the surface heat transfer coefficient. There are no qualitative changes in the bifurcation diagram except in the limit where both the surface heat flux and fresh-water flux are prescribed. The bifurcation structure at large aspect ratio is shown to converge to that obtained by asymptotic theory. The complete structure of symmetric and asymmetric multiple equilibria is shown to originate from a codimension-three bifurcation, which arises through the intersection of a cusp and the codimension-two singularity responsible for symmetry breaking.

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26

Shablovsky, Ya О. "Rarе Fedorov groups in structural mineralogy." МИНЕРАЛОГИЯ (MINERALOGY) 5 (July 16, 2019): 3–9. http://dx.doi.org/10.35597/2313-545x-2019-5-2-3-9.

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The crystal order in structure of a solid phase is provided by the symmetry of interatomic interactions. In its turn, the latter causes the symmetry of atomic spatial positions, i.e. the spatial symmetry of the structure. From this viewpoint, the phenomenon of mineral formation can formally be considered as a result of ordering the atoms by the operations of spatial symmetry. This ordering is selective. Most mineral structures are described by minor formally possible spatial symmetry groups. The peculiarities of «structural preferences» of mineral phases during crystallization and re-crystallization are studied. The quantitative estimations for frequencies of Fedorov groups in crystal structures are given.

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27

Meierbachtol, Adam, Eric Rohman, Eric Paur, John Bottoms, and Marc Tompkins. "Quantitative Improvements in Hop Test Scores After a 6-Week Neuromuscular Training Program." Sports Health: A Multidisciplinary Approach 9, no. 1 (September 20, 2016): 22–29. http://dx.doi.org/10.1177/1941738116667933.

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Background: In patients who have undergone anterior cruciate ligament reconstruction (ACLR), the effect of neuromuscular re-education (NMR) programs on standard hop tests outcomes, including limb symmetry indices (LSIs), is unknown. Hypothesis: Both legs will show improvement in hop test–measured units after neuromuscular training, but the involved leg will show relatively greater improvement leading to improved limb symmetry. Patients younger than 18 years will show more improvement than patients who are older. Study Design: Retrospective cohort study. Level of Evidence: Level 3. Methods: Patients self-selected their participation in this NMR program, which was completed after traditional outpatient physical therapy. Pre– and post–hop test scores were recorded as the primary outcome measure. Results: Seventy-one patients met the inclusion criteria and completed hop testing. Overall, the involved leg showed significant improvements (pretest/posttest) for single-leg hop (138.30 cm/156.89 cm), triple crossover hop (370.05 cm/423.11 cm), and timed hop (2.21 s/1.99 s). Similarly, on the uninvolved leg, improvements were seen for the single-leg hop (159.30 cm/171.87 cm) and triple crossover hop (427.50 cm/471.27 cm). Overall mean limb symmetry improved across all 4 hop tests, but there was significant improvement only on the single-leg hop (87% pretest to 92% posttest). Patients younger than 18 years showed mean significant LSI improvement on the triple crossover hop. Conclusion: Utilizing an intensive 6-week NMR program after ACLR prior to return to sport can improve quantitative hop test measurements. Patients younger than 18 years had greater improvement than those 18 years and older. Clinical Relevance: Advanced NMR programs can be successfully utilized in the postoperative ACLR setting to improve quantitative limb symmetry.

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Mckearney, Richard M., John V. Williams, and Nigel S. Mercer. "Quantitative Computer-Based Assessment of Lip Symmetry following Cleft Lip Repair." Cleft Palate-Craniofacial Journal 50, no. 2 (March 2013): 138–43. http://dx.doi.org/10.1597/11-227.

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29

Qi Guo, Falei Guo, and Jiaqing Shao. "Irregular Shape Symmetry Analysis: Theory and Application to Quantitative Galaxy Classification." IEEE Transactions on Pattern Analysis and Machine Intelligence 32, no. 10 (October 2010): 1730–43. http://dx.doi.org/10.1109/tpami.2010.13.

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30

Yogev-Einot, Dina, and David Avnir. "Quantitative Symmetry and Chirality of the Molecular Building Blocks of Quartz." Chemistry of Materials 15, no. 2 (January 2003): 464–72. http://dx.doi.org/10.1021/cm0207806.

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31

Faure, P. A., and R. R. Hoy. "Auditory symmetry analysis." Journal of Experimental Biology 203, no. 21 (November 1, 2000): 3209–23. http://dx.doi.org/10.1242/jeb.203.21.3209.

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The study of biological symmetry continues to be an important and active area of research, yet in the hearing sciences there are no established quantitative methods for measuring auditory asymmetries and dissimilarities in threshold tuning curves (i.e. audiograms). Using a paired design and adopting methods from the analysis of fluctuating asymmetry, we describe methods for auditory researchers interested in delineating auditory asymmetries and comparing tuning curves, behavioral or neural. We illustrate the methods using audiograms of the prothoracic T-cell interneuron in a nocturnal katydid (Neoconocephalus ensiger). The results show that 87–92 % of T-cells had right-minus-left threshold asymmetries no larger than expected from measurement error alone. Thus, apart from small random fluctuating asymmetries, T-cell pairs in N. ensiger showed no sensory bias and were bilaterally symmetrical from 5 to 100 kHz. The sensitivity of the methods for detecting tuning curve dissimilarities was confirmed in a sound lateralization paradigm by comparing the ‘symmetry’ (i.e. similarity) of T-cell tuning curves measured at 0 degrees stimulation with tuning curves measured at 90 degrees stimulation for the same T-cell. The results show that T-cell thresholds measured frontally (0 degrees) were significantly higher than those measured laterally (90 degrees), particularly for ultrasonic frequencies. Statistically, the directional shift (increase) in auditory thresholds was detected as a directional asymmetry in T-cell tuning, whose origin and functional significance to an insect behaving normally are discussed. The paper discusses practical considerations for detecting auditory asymmetries and tuning curve dissimilarities in general, and closes by questioning the relevance of auditory symmetry for sound localization in both vertebrates and insects.

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NAPSUCIALE, M., and S. RODRIGUEZ. "UA(1) SYMMETRY BREAKING AND THE SCALAR SECTOR OF QCD." International Journal of Modern Physics A 16, no. 17 (July 10, 2001): 3011–24. http://dx.doi.org/10.1142/s0217751x01004189.

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It is shown that most of the unusual properties of the lowest lying scalar (and pseudoscalar) mesons can be understood, at the qualitative and quantitative level, on the basis of the breakdown of the UA(1) symmetry coupled to the vacuum expectation values of scalars by the spontaneous breaking of chiral symmetry.

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33

Hsiao, Yu-Ching, and Jing-Jing Fang. "An Automatic Voxel-Based Method for Optimal Symmetry Plane Generation for the Maxillofacial Region in Severe Asymmetry Cases." Journal of Clinical Medicine 11, no. 19 (September 26, 2022): 5689. http://dx.doi.org/10.3390/jcm11195689.

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Symmetry is representative of aesthetics and health in all kinds of vertebrates, especially the human face. Therefore, to automatically locate the appropriate symmetry plane is crucial. The aim of this study was to develop an automatic and reliable method to determine the symmetry plane of the maxillofacial region. We compared the proposed method of determining the symmetry plane by assessing landmark-based and surface-based methods by way of quantitative symmetry assessments. Statistical analysis was applied to evaluate whether significant difference existed among these three kinds of symmetry planes. Twenty cases who had a diagnosis of severe facial asymmetry were evaluated retrospectively. The results showed that searching for the symmetry plane using a voxel-based method, named the optimal symmetry plane (OSP), achieved the most representative symmetry according to the outcomes of the trials. The OSP was significantly more symmetrical than the other two planes, as determined by other methods. The paired-voxel computation method proposed in this research is a robust and reliable method for identifying the unique symmetry plane for patients with severe facial asymmetry. Symmetry is of crucial significance for all kinds of vertebrates, including its clinical implications for surgical planning in orthognathic surgery.

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34

Weathers, William M., David Khechoyan, Erik M. Wolfswinkel, Kriti Mohan, Andrew Nagy, Robert J. Bollo, Edward P. Buchanan, and Larry H. Hollier. "A Novel Quantitative Method for Evaluating Surgical Outcomes in Craniosynostosis: Pilot Analysis for Metopic Synostosis." Craniomaxillofacial Trauma & Reconstruction 7, no. 1 (March 2014): 1–7. http://dx.doi.org/10.1055/s-0033-1356758.

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Objective assessment of head shape has been an elusive goal in the management of craniosynostosis patients. Clinical judgment, craniometric indices, and computed tomography scans are the primary means through which a surgeon assesses this patient population. The purpose of this study was to examine and discuss the utility of the STARscanner for evaluation of surgical outcomes in metopic synostosis patients. A retrospective chart review of patients with metopic synostosis who underwent fronto-orbital advancement with pre- and postoperative STARscanner imaging at Texas Children's Hospital was performed. Two patients were identified and evaluation and discussion of the data produced by the STARscanner was undertaken. A novel symmetry index created by the authors, called the anterior–posterior volume ratio (APVR), was discussed for use in metopic synostosis patients. The postoperative growth metrics demonstrated an interval increase compared with the preoperative data. The anterior symmetry ratio, posterior symmetry ratio, overall symmetry ratio, cranial vault volumes, cranial vault asymmetry index, and cephalic ratio were not found to be useful in evaluating resolution of dysmorphology after fronto-orbital advancement in metopic synostosis. The APVR does not characterize dysmorphology, but may help show degree of expansion of the anterior cranial vault after fronto-orbital advancement. The STARscanner imaging device does not appear to have significant utility in characterizing head shape for surgical outcomes assessment in metopic synostosis. The minor utility of this device may be that it is a safe and fast way to derive growth parameters for both short-term and long-term follow-up of cranial vault remodeling.

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35

Graebner, Melissa E., Fabrice Lumineau, and Darcy Fudge Kamal. "Unrequited: Asymmetry in interorganizational trust." Strategic Organization 18, no. 2 (November 4, 2018): 362–74. http://dx.doi.org/10.1177/1476127018808465.

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Many studies of interorganizational relationships assume that trust between organizations is symmetric. In this essay, we explore the origins of this assumption and examine relevant quantitative and qualitative evidence from the literatures on strategy, marketing, supply chain management, and information systems. We conclude that no systematic evidence currently exists to support the assumption that interorganizational trust is typically symmetric. We explore how the possibility of asymmetry complicates interpretation of previous research on the effects of interorganizational trust. We encourage further research to identify conditions under which symmetry is likely, and offer a variety of strategies that scholars may use to deal with potential asymmetry.

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36

Kim, Kyou-Hyun, David A. Payne, and Jian Min Zuo. "Determination of fluctuations in local symmetry and measurement by convergent beam electron diffraction: applications to a relaxor-based ferroelectric crystal after thermal annealing." Journal of Applied Crystallography 46, no. 5 (September 18, 2013): 1331–37. http://dx.doi.org/10.1107/s0021889813022097.

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Single crystals of Pb(Mg1/3Nb2/3)O3–31%PbTiO3(PMN–31%PT) are known for their complex domain structures at the nanometre scale. While their average symmetry has been studied by X-ray, neutron and electron diffraction methods, there is little knowledge about variations in symmetry at the local scale. Here, direct evidence is provided for the volume dependence and spatial dependence of symmetry fluctuations by using quantitative convergent beam electron diffraction and energy dispersive X-ray spectroscopy. Fluctuations in symmetry were determined by using different electron beam probe sizes ranging from ∼2 to 25 nm from a crystal ∼62 nm thick. The symmetry of PMN–31%PT was found to increase linearly as the average volume increased, and the local symmetry fluctuated from one location to another at the nanoscale. Energy dispersive X-ray spectroscopy indicates that chemical fluctuations are significant when the probe size decreases to ∼2 nm. The symmetry fluctuation is attributed to locally varying composition-dependent ionic displacements and spontaneous polarization.

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Yang, Jishi, Yaolu Liu, Dongyang Sun, Ning Hu, and Huiming Ning. "Inverse Design of Valley-Like Edge States of Sound Degenerated Away from the High-Symmetry Points in a Square Lattice." Materials 15, no. 19 (September 27, 2022): 6697. http://dx.doi.org/10.3390/ma15196697.

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Robust edge states of periodic crystals with Dirac points fixed at the corners or centers of the Brillouin zones have drawn extensive attention. Recently, researchers have observed a special edge state associated with Dirac cones degenerated at the high symmetric boundaries of the first irreducible Brillouin zone. These nodal points, characterized by vortex structures in the momentum space, are attributed to the unavailable band crossing protected by mirror symmetry. By breaking the time reversal symmetry with intuitive rotations, valley-like states can be observed in a pair of inequivalent insulators. In this paper, an improved direct inverse design method is first applied to realize the valley-like states. Compared with the conventional strategy, the preparation of transition structures with degeneracy points is skipped. By introducing the quantitative gauge of mode inversion error, insulator pairs are directly obtained without manually tuning the structure with Dirac cone features.

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Wu, Jianning, and Bin Wu. "The Novel Quantitative Technique for Assessment of Gait Symmetry Using Advanced Statistical Learning Algorithm." BioMed Research International 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/528971.

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The accurate identification of gait asymmetry is very beneficial to the assessment of at-risk gait in the clinical applications. This paper investigated the application of classification method based on statistical learning algorithm to quantify gait symmetry based on the assumption that the degree of intrinsic change in dynamical system of gait is associated with the different statistical distributions between gait variables from left-right side of lower limbs; that is, the discrimination of small difference of similarity between lower limbs is considered the reorganization of their different probability distribution. The kinetic gait data of 60 participants were recorded using a strain gauge force platform during normal walking. The classification method is designed based on advanced statistical learning algorithm such as support vector machine algorithm for binary classification and is adopted to quantitatively evaluate gait symmetry. The experiment results showed that the proposed method could capture more intrinsic dynamic information hidden in gait variables and recognize the right-left gait patterns with superior generalization performance. Moreover, our proposed techniques could identify the small significant difference between lower limbs when compared to the traditional symmetry index method for gait. The proposed algorithm would become an effective tool for early identification of the elderly gait asymmetry in the clinical diagnosis.

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Inoue, S., V. Frank, M. Hörning, S. Kaufmann, H. Y. Yoshikawa, J. P. Madsen, A. L. Lewis, S. P. Armes, and M. Tanaka. "Live cell tracking of symmetry break in actin cytoskeleton triggered by abrupt changes in micromechanical environments." Biomaterials Science 3, no. 12 (2015): 1539–44. http://dx.doi.org/10.1039/c5bm00205b.

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Bormashenko, Edward. "Entropy, Information, and Symmetry: Ordered is Symmetrical." Entropy 22, no. 1 (December 19, 2019): 11. http://dx.doi.org/10.3390/e22010011.

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Entropy is usually understood as the quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are definitely obscure. This leads to numerous misinterpretations of entropy. We propose to see the disorder as an absence of symmetry and to identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into an initially disordered physical system. We demonstrate with the binary system of elementary magnets that introducing elements of symmetry necessarily diminishes its entropy. This is true for one-dimensional (1D) and two-dimensional (2D) systems of elementary magnets. Imposing symmetry does not influence the Landauer principle valid for the addressed systems. Imposing the symmetry restrictions onto the system built of particles contained within the chamber divided by the permeable partition also diminishes its entropy.

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Andrews, David L. "Irreducible Cartesian Tensor Analysis of Harmonic Scattering from Chiral Fluids." Symmetry 12, no. 9 (September 7, 2020): 1466. http://dx.doi.org/10.3390/sym12091466.

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Symmetry principles of several distinct kinds are revealingly engaged in an analysis focussing on third harmonic scattering, a current focus of research on nonlinear optics in chiral media. Analysis in terms of irreducible Cartesian tensors elucidates the detailed electrodynamical origin and character of the corresponding material properties. Considerations of fundamental charge, parity and time reversal (CPT) symmetry reveal the conditions for an interplay of transition multipoles to elicit a chiral response using circularly polarised pump radiation, and the symmetry of quantised angular momentum underpins the associated selection rules and angular distribution. The intrinsic structural symmetry of chiral scatterers determines their capacity to exhibit differential response. Exploiting permutational index symmetry in the response tensors enables quantitative assessment of the boundary values for experimentally measurable properties, including circular intensity differentials.

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SCHIPPERS, MICHAEL. "STRUCTURAL PROPERTIES OF QUALITATIVE AND QUANTITATIVE ACCOUNTS TO COHERENCE." Review of Symbolic Logic 7, no. 3 (July 18, 2014): 579–98. http://dx.doi.org/10.1017/s1755020314000227.

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AbstractThis paper evaluates four different qualitative (probabilistic) accounts to coherence with a focus on structural properties (symmetries, asymmetries, and transitivity). It is shown that while coherence is not transitive on any of these accounts, there are screening-off conditions that render coherence transitive. In a second step, an array of quantitative (probabilistic) accounts to coherence is considered. The upshot is that extant measures differ considerably with respect to a number of symmetry constraints.

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Pfau, Thilo, W. Michael Scott, and Tabitha Sternberg Allen. "Upper Body Movement Symmetry in Reining Quarter Horses during Trot In-Hand, on the Lunge and during Ridden Exercise." Animals 12, no. 5 (February 27, 2022): 596. http://dx.doi.org/10.3390/ani12050596.

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Veterinary lameness examinations often comprise assessing ridden horses. Quantitative movement symmetry measurements can aid evidence-based decision making. While these are available for ‘English’ style riding, they are not for ‘Western’ style riding. This quantitative observational study quantified movement symmetry in reining Quarter Horses (QHs). Movement symmetry of the head, withers and sacrum (differences between minima, maxima and upward amplitudes) were quantified with inertial sensors in N = 30 medium/high level reining QHs during trot in-hand, on the lunge and ridden by one experienced rider (straight-line/circles) on reining-purpose riding surfaces. Mixed linear models for movement symmetry assessed the effects of ridden exercise and movement direction (fixed factors), stride time (covariate) and horse (random factor): single factors and two-way interactions with Bonferroni correction at p < 0.05. Three withers and pelvic parameters showed marginally more symmetrical movement when ridden (p ≤ 0.044; 1–5 mm differences). Three withers, three sacrum and one head parameter were significantly affected by movement direction (all p ≤ 0.026), five showed increased asymmetry on the inside rein, and two, quantifying vertical displacement maximum difference, showed the opposite. Riding QHs in ‘Western’ style showed small movement symmetry differences. Circular exercise confirmed increases in weight bearing asymmetry on the inside rein and in pushoff asymmetry on the outside rein. This should be further investigated for differentiating between different causes of lameness.

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Peter, Roman, Bart J. Emmer, Adriaan C. G. M. van Es, and Theo van Walsum. "Quantitative Analysis of Geometry and Lateral Symmetry of Proximal Middle Cerebral Artery." Journal of Stroke and Cerebrovascular Diseases 26, no. 10 (October 2017): 2427–34. http://dx.doi.org/10.1016/j.jstrokecerebrovasdis.2017.05.039.

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Keinan, Shahar, and David Avnir. "Studies in copper(II) complexes: correlations between quantitative symmetry and physical properties." Journal of the Chemical Society, Dalton Transactions, no. 6 (2001): 941–47. http://dx.doi.org/10.1039/b009638p.

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Vincent, R. "Quantitative energy-filtered electron diffraction." Proceedings, annual meeting, Electron Microscopy Society of America 52 (1994): 992–93. http://dx.doi.org/10.1017/s0424820100172693.

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Microanalysis and diffraction on a sub-nanometre scale have become practical in modern TEMs due to the high brightness of field emission sources combined with the short mean free paths associated with both elastic and inelastic scattering of incident electrons by the specimen. However, development of electron diffraction as a quantitative discipline has been limited by the absence of any generalised theory for dynamical inelastic scattering. These problems have been simplified by recent innovations, principally the introduction of spectrometers such as the Gatan imaging filter (GIF) and the Zeiss omega filter, which remove the inelastic electrons, combined with annual improvements in the speed of computer workstations and the availability of solid-state detectors with high resolution, sensitivity and dynamic range.Comparison of experimental data with dynamical calculations imposes stringent requirements on the specimen and the electron optics, even when the inelastic component has been removed. For example, no experimental CBED pattern ever has perfect symmetry, departures from the ideal being attributable to residual strain, thickness averaging, inclined surfaces, incomplete cells and amorphous surface layers.

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Dresp-Langley, Birgitta. "Bilateral Symmetry Strengthens the Perceptual Salience of Figure against Ground." Symmetry 11, no. 2 (February 14, 2019): 225. http://dx.doi.org/10.3390/sym11020225.

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Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a “foreground”-“background” choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength of figure-ground in triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of “foreground” judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations.

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Viswanathan, R., J. Garnaes, D. K. Schwartz, and J. A. N. Zasadzinski. "Quantitative AFM of langmuir-blodgett films." Proceedings, annual meeting, Electron Microscopy Society of America 51 (August 1, 1993): 510–11. http://dx.doi.org/10.1017/s0424820100148381.

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Because of their applications in the areas of non-linear optics, molecular electronics, and biosensors, Langmuir-Blodgett (LB) films have been extensively studied by a wide variety of scattering and spectroscopic techniques. The atomic force microscope has emerged as an important tool for studying LB films because of its unprecedented ability to quantitatively measure films with high resolution.The unique abilities of quantitative AFM imaging motivated us to investigate the effect of incorporating different divalent metal cations and fatty acids of different chain length into films deposited on both amorphous and ordered substrates. Once substrate effects have been accounted for, multilayer Langmuir-Blodgett films of palmitic, stearic and arachidic acid salts show that the area per molecule is primarily controlled by the detailed interactions of the counterion with the carboxylic acid group. However, the lattice dimensions and symmetry are dictated by the close packing of the alkane chains, given the constraint of area per molecule set by the counterion.

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Peckett, A. "Quantitative colours of opaque minerals." Mineralogical Magazine 53, no. 369 (March 1989): 71–78. http://dx.doi.org/10.1180/minmag.1989.053.369.07.

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AbstractAnisotropic opaque minerals viewed in reflected light microscopy show two sets of colours: the colours seen in plane polarized light which change as the section is rotated on the microscope stage, and the colours seen between crossed polars which change as the analyser is uncrossed. These latter colours are known variously as polarization colours or anisotropic rotation tints, but are here referred to as anisotropy colours. They are commonly a diagnostic aid to correct mineral identification. All these colours occur as a consequence of the dispersion of the relative permittivity (dielectric) tensor—the variation in the values of the tensor with wavelength of incident light and in low symmetry crystals, the variation in the directions of the principal axes of the tensor with wavelength.In this paper, it is shown that the colour seen in plane polarized light and the anisotropy colours can be predicted for any orientation of section, at any stage angle, and for any degree of uncrossing of the analyser by calculations based on the dielectric tensor values, and these predicted colours compare favourably with the observed values. Three minerals are studied in this paper as examples: stannite, covelline, and bournonite.

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Zheng, Mingliang. "Quantitative Analysis for the Spread Range of Malignant Tumor Based on Lie Symmetry." Complexity 2020 (April 15, 2020): 1–6. http://dx.doi.org/10.1155/2020/8468024.

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It provided a powerful new way for predicting the growth trend of malignant tumor and assisting the treatment of cancer patients. Firstly, a one-dimensional mathematical model for the dynamic proliferation of malignant tumors is established on the premise of related simplification and hypothesis. Secondly, according to the Lie symmetry theory, we deduce the multigroup allowed infinitely small generating elements of partial differential equations and obtain the analytic form of the exact invariant solution. Finally, the influence of the model condition parameters (oxygen concentration and inhibitor concentration) on the tumor multiplication time index T is analyzed and discussed. The results showed that when the concentration of the nutrient substance is higher than the critical concentration, the multiplication time of the tumor region approximately decreased firstly and then increased in the linear form about tumor radius under different oxygen concentrations, and at the same radius, the oxygen concentration is lower, and the multiplication time is longer; the multiplication time of the tumor region approximately decreased in the exponential form about tumor radius under different inhibitor concentrations, and at the same radius, the inhibitor concentration is higher, and the multiplication time is bigger, which are consistent with the experimental and clinical observation.

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