Relevant bibliographies by topics / Quantitative symmetry

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Quantitative symmetry'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Quantitative symmetry"

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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Quantitative symmetry"

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RONCORONI, ALBERTO. "Symmetry and quantitative stability results for problems in geometric analysis and functional inequalities." Doctoral thesis, Università degli studi di Pavia, 2019. http://hdl.handle.net/11571/1292128.

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The thesis addresses the characterization of geometric properties for problems in Partial Differential Equations (PDEs), geometric analysis and functional inequalities, with a particular interest in the study of symmetry and quantitative stability issues.
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Simonetti, Emeline. "Contribution au développement et à la validation de méthodes fondées sur la technologie embarquée pour l'analyse quantitative de la locomotion et la rééducation fonctionnelle de la personne amputée de membre inférieur." Thesis, Paris, HESAM, 2020. http://www.theses.fr/2020HESAE052.

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Un des objectifs majeurs de la rééducation des personnes amputées de membre inférieur appareillées est le retour à une marche physiologique, efficace énergétiquement et minimisant le risque de chutes lié à la perte d’équilibre. Peu d’outils cliniques permettent aujourd’hui de quantifier ces aspects de la locomotion. L’émergence de capteurs embarqués miniaturisés offre des opportunités pour la description quantitative et écologique de la marche. Dans ce contexte, l’objectif de la thèse était de contribuer au développement de protocoles embarqués pour apporter des données quantitatives pertinentes lors de la rééducation à la marche des personnes amputées de membre inférieur. Deux approches complémentaires ont été adoptées. La première approche consiste à utiliser un modèle biomécanique du corps afin d’extraire des descripteurs quantifiés pertinents. Un protocole permettant d’estimer l’accélération et la vitesse instantanée du centre de masse à partir de 5 centrales inertielles a ainsi été proposé à partir d’une analyse préliminaire sur les données de marche de dix personnes amputées transfémorales et a été validé chez une personne amputée transfémorale. La seconde approche consiste à extraire des paramètres concis par traitement du signal des données brutes des capteurs. La fiabilité et la pertinence clinique de la quantification de tels paramètres pour caractériser la symétrie et l’équilibre de la marche ont été étudiées pour la première fois chez les personnes amputées de membre inférieur. L’ensemble des travaux produits au cours de cette thèse contribue ainsi au transfert vers la clinique des outils embarqués d’analyse du mouvement par l’identification de paramètres biomécaniques et cliniques pertinents et la validation d’algorithmes originaux permettant la quantification de la marche des amputés de membre inférieur
One key objective during the rehabilitation of people with lower-limb amputation fitted with a prosthesis is the restoration of a physiological and energy-efficient gait pattern minimizing falling risks due to the loss of balance. Few practical tools are available to provide quantitative data to assist the follow-up of patients in the clinical routine. The development of wearable sensors offers opportunities to quantitatively and objectively describe gait in ecological situations. In this context, the aim of the thesis is to contribute to the development of wearable tools and protocols to support the functional rehabilitation of lower-limb amputees by providing clinically relevant quantitative data. Two complementary approaches have been implemented. The first approach consists in developing biomechanical models of the human body in order to retrieve biomechanically founded parameters. A protocol allowing to accurately estimate the body center of mass acceleration and instantaneous velocity has therefore been proposed based on gait data of ten people with transfemoral amputation and was validated in one person with transfemoral amputation. The second approach consists in identifying patterns in the signals measured by wearable sensors to extract concise descriptors of gait symmetry and dynamic balance. The clinical relevance and reliability of these descriptors have been investigated for the first time in people with lower-limb amputation. The work produced in the course of this thesis has contributed to the clinical transfer of wearable sensors into the clinical practice through the identification of clinically and biomechanically relevant parameters and the validation of original algorithms allowing to quantitatively describe the gait of lower-limb amputees
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Carvajales, Goyetche Leon Seibal. "Quantitative aspects of Anosov subgroups acting on symmetric spaces." Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS021.

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L’objet de cette thèse est l’étude du problème de comptage orbitale pour des couples symétriques pseudo-Riemanniens sous l’action des sous-groupes de type Anosov du groupe de Lie sous-jacent. Premièrement nous étudions ce problème pour le couple symétrique (PSO(p,q), PSO(p,q−1)) et un sous-groupe de PSO(p,q) de type projectivement Anosov . Nous regardons l’orbite d’une copie géodésique de l’espace symétrique Riemannien de PSO(p,q−1) dans l’espace symétrique Riemannien de PSO(p,q). Nous prouvons un comportement asymptotique purement exponentiel, lorsque t tend vers l’infini, pour le nombre d’éléments dans cette orbite qui sont à distance plus petit que t de la copie géodésique originale. Nous interprétons ce résultat comme le comportement asymptotique du nombre de segments géodésiques de type espace (dans l’espace hyperbolique pseudo-Riemannien) de longueur maximale t dans l’orbite d’un point base. Nous prouvons des résultats analogues pour d’autres fonctions de comptage. Ensuite nous regardons le couple symétrique (PSL(d,R), PSO(p,d−p)) et un sous-groupe Borel-Anosov de PSL(d,R). Nous présentons des contributions vers la compréhension du comportement asymptotique de la fonction de comptage associée à une copie géodésique de l’espace symétrique Riemannien de PSO(p,d-p) dans l’espace symétrique Riemannien de PSL(d,R)
This thesis addresses the study of the orbital counting problem for pseudo-Riemannian symmetric pairs under the action of Anosov subgroups of the underlying Lie group. In the first part we study this problem for the pair (PSO(p,q), PSO(p,q−1)) and a projective Anosov subgroup of PSO(p,q). We look at the orbit of a geodesic copy of the Riemannian symmetric space of PSO(p,q−1) inside the Riemannian symmetric space of PSO(p,q). We show a purely exponential asymptotic behavior, as t goes to infinity, for the number of elements in this orbit which are at distance at most t from the original geodesic copy. We then interpret this result as the asymptotic behavior of the amount of space-like geodesic segments (in the pseudo-Riemannian hyperbolic space) of maximum length t in the orbit of a basepoint. We prove analogue results for other related counting functions. In the second part we look at the pair (PSL(d,R), PSO(p,d−p)) and a Borel-Anosov subgroup of PSL(d,R), presenting contributions towards the understanding of the asymptotic behavior of the counting function associated to a geodesic copy of the Riemannian symmetric space of PSO(p,d-p) inside the Riemannian symmetric space of PSL(d,R)
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Hauri, Brian R. "A quantitative analysis of symmetry, fluency, and pattern preference." 2013. http://hdl.handle.net/1993/22031.

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People prefer symmetric over asymmetric patterns (Reber, Schwarz, & Winkielman, 2004). According to the fluency attribution perspective, this preference reflects differences in processing speed where increased processing efficiency leads to increased pattern preference. To test the account, in Experiment 1, participants’ speed of response to a pattern predicted the relationship between pattern symmetry and pattern preference. Experiment 2 expanded this account and found that a second measure of processing efficiency, recognition accuracy for patterns, predicted the relationship between pattern symmetry and pattern preference. Experiment 3 tested the attribution account of the fluency attribution hypothesis. Participants made a judgment of pattern mood rather than pattern preference. Despite a change of judgment task to an unintuitive judgment of pattern mood, participants attributed increased processing efficiency for patterns to increased pattern happiness. The three experiments provide an integration of the information processing and fluency attribution perspectives to account for symmetry preference judgments.
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Poggesi, Giorgio. "The Soap Bubble Theorem and Serrin's problem: quantitative symmetry." Doctoral thesis, 2019. http://hdl.handle.net/2158/1151383.

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Tseng, Chuan-Che, and 曾川哲. "Quantitative Evaluation of Stroke Patient''s Gait Symmetry Based on Sequential Image Analysis." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/ry48n9.

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碩士
國立臺北科技大學
電腦與通訊研究所
98
One stroke patient is not only to much affect his physical and mental state but also heavily inflict the body and mind of patient’s family member. Therefore, our major subject of this study is to design an auxiliary tool for the evaluation after the stroke patient rehabilitation and then promoting a better life quality of the patient’s family. Our system employs the gait analysis algorithm to offer the quantized gait information through the vision base. Hence, our system can provide the gait state for the stroke patient himself. Moreover, the rehabilitation goal will be obvious such that it highly promote the rehabilitation volition for the stroke patients. Our system owns the two advantages of the portable and low-cost characteristics. Therefore, our design of the gait analysis system can be indeed applied to hospitals, organizations, or homes for the rehabilitation evaluation. Meanwhile, our system is consisting of the low-cost consumer products, a video camera, PC, and simple electronic components. There are 3 phases in our design of the gait symmetry evaluation. First, our system uses the video camera to track and record the track of the marked LED points for getting the gait image of the stroke patient. These marked tracks are recorded within a gait video file, and then it will be analyzed by our algorithm on PC. The second phase is called the quantization and analysis stage. The gotten gait video file can be analyzed by our gait analysis algorithm, and then we can obtain the quantization of the gait information. The third phase is called the information service stage. The therapists can offer the objective gait analysis results to the stroke patient as the next rehabilitation suggestions. Our system has been verified by the experiment and analysis gaits of 12 stroke patients and 6 healthy persons. Our experiment results indicate that our system can effective offer an auxiliary tool for the evaluation after the stroke patient rehabilitation.
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Wu, Chung-Yi, and 吳崇溢. "Quantitative Analysis of Gait Initiation and Symmetry from Tracking Parkinsonian Patients' Walking in Monocular Image Sequences." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/36307326707572755912.

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碩士
國立交通大學
電機與控制工程系所
97
Parkinson’s disease (PD) is a neurodegenerative disease of central nervous system which causes motor fluctuations and gait is considered as the major hallmark of PD. Nowadays, the assessment of specific gait disturbances of gait initiation and symmetry is an important issue in clinical neurological diseases. Neuro-degeneration in PD patients increases the deficiencies in regulating the locomotion and challenges initiation of gait. Therefore, we want to develop an objective and quantitative gait analysis method for assisting clinicians with assessing massive PD patients in the severity of gait initiation and symmetry. The proposed image-based system utilizes a Centroid Tracking algorithm to localize the positions of knee and ankle, extracts knee angle signal and obtains quantitative gait parameters and associated symmetry indexes in first step duration and stable condition. In first step duration and stable condition, the results demonstrate that the statistical differences of swing length and velocity between age-matched normal subjects and PD patients before drug treatment and between PD patients before and after drug treatment are confirmed by t-test (p<0.05). Besides, the symmetry indexes of swing length and swing speed also have statistical differences between normal subjects and PD patients before and after drug treatment. The further relationship between gait parameters and the Unified Parkinson Disease Rating Scales (UPDRS) is investigated. The UPDRS sub-scores: Gait & Posture, Leg Agility and Body Bradykinesia have significant correlation coefficients of -0.5978, -0.5909 and -0.6362 with swing length and -0.6033, -0.5725 and -0.6566 with velocity. These results can further explain the variations of postural reaction and bradykinesia. The developed system is proved to be correlated with some clinical symptoms and provides a quantitative method in the assessment of parkinsonian gait.
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Books on the topic "Quantitative symmetry"

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Coopersmith, Jennifer. Antecedents. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0002.

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Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the Bernoullis, Leibniz, Maupertuis, Euler, and d’Alembert. Also, Stevin was the first to invoke the impossibility of perpetual motion in a proof, and Huygens was the first to put Galilean Relativity to a quantitative test. The Swiss family of mathematical geniuses, the Bernoullis, tackled isoperimetric problems, such as the brachystochrone, and Johann Bernoulli discovered the Principle of Virtual Velocities. The flavour of the eighteenth century is shown in the evocative tale of the König affair, and the correspondence between Daniel Bernoulli and Euler. It is shown how symmetry arguments, leading ultimately to an energy-analysis, were competing with Newton’s force-analysis. The Principle of Least Action and Variational Mechanics, proper, were developed by Lagrange, Hamilton, and Jacobi.
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Book chapters on the topic "Quantitative symmetry"

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Nishisato, Shizuhiko. "Mathematical Symmetry." In Behaviormetrics: Quantitative Approaches to Human Behavior, 49–57. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9170-6_5.

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Nishisato, Shizuhiko. "Optimality and Symmetry." In Behaviormetrics: Quantitative Approaches to Human Behavior, 3–8. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9170-6_1.

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Nishisato, Shizuhiko. "Space Theory and Symmetry." In Behaviormetrics: Quantitative Approaches to Human Behavior, 69–81. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9170-6_7.

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Evans, Nick. "Electroweak Symmetry Breaking from the Top." In Quantitative Particle Physics: Cargèse 1992, 407–12. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4615-2944-6_12.

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Walsh, T. D., and R. Vincent. "Quantitative measurement of symmetry in CBED patterns." In Electron Microscopy and Analysis 1997, 141–44. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003063056-36.

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Mignogna, R. B. "Ultrasonic Determination of Elastic Constants from Oblique Angles of Incidence in Non-Symmetry Planes." In Review of Progress in Quantitative Nondestructive Evaluation, 1565–72. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-5772-8_201.

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Aristégui, Christophe, and Stéphane Baste. "Load-Induced Change in the Elastic Symmetry of a Ceramic Matrix Composite Under Off-Axis Tensile Loading." In Review of Progress in Quantitative Nondestructive Evaluation, 1131–38. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5339-7_146.

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Aristégui, Christophe, and Stéphane Baste. "Determination of Angular Parallaxes between the Geometric Coordinate System and the Material Symmetry Coordinate System of Anisotropic Materials." In Review of Progress in Quantitative Nondestructive Evaluation, 1677–84. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-0383-1_219.

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Wild, Paul, and Lutz Schröder. "A Quantified Coalgebraic van Benthem Theorem." In Lecture Notes in Computer Science, 551–71. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_28.

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AbstractThe classical van Benthem theorem characterizes modal logic as the bisimulation-invariant fragment of first-order logic; put differently, modal logic is as expressive as full first-order logic on bisimulation-invariant properties. This result has recently been extended to two flavours of quantitative modal logic, viz. fuzzy modal logic and probabilistic modal logic. In both cases, the quantitative van Benthem theorem states that every formula in the respective quantitative variant of first-order logic that is bisimulation-invariant, in the sense of being nonexpansive w.r.t. behavioural distance, can be approximated by quantitative modal formulae of bounded rank. In the present paper, we unify and generalize these results in three directions: We lift them to full coalgebraic generality, thus covering a wide range of system types including, besides fuzzy and probabilistic transition systems as in the existing examples, e.g. also metric transition systems; and we generalize from real-valued to quantale-valued behavioural distances, e.g. nondeterministic behavioural distances on metric transition systems; and we remove the symmetry assumption on behavioural distances, thus covering also quantitative notions of simulation.
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Noster, Norbert, Arnon Hershkovitz, Michal Tabach, and Hans-Stefan Siller. "Learners’ Strategies in Interactive Sorting Tasks." In Lecture Notes in Computer Science, 285–98. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16290-9_21.

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AbstractUsing examples and non-examples is a common technique to demonstrate concepts’ characteristics and boundaries. Based on their properties, certain objects are accepted as examples or non-examples intuitively, while others are accepted or neglected non-intuitively. This 2*2 classification is powerful when designing technology-enhanced learning experiences in which feedback could be provided in real-time. That is, feedback could be based not only on the correctness of student response, but also on the specifics of the objects with which they were engaged. Following this framework, we developed an interactive sorting task that aims at strengthening elementary school students’ understanding of reflective symmetry. We studied learners’ interaction with the objects presented to them, and their success. Our study included 29 elementary school students (ages 9 to 12) from both Israel and Germany. We used screen recording to code participants’ shape-movements, and defined quantitative measures of these movements. Our findings support the need for designing feedback that takes into consideration object’s properties and students’ behavior.
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Conference papers on the topic "Quantitative symmetry"

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Sun, Miao. "Visco-elastic constant recovery in the absence of known material symmetry." In QUANTITATIVE NONDESTRUCTIVE EVALUATION. AIP, 2002. http://dx.doi.org/10.1063/1.1472961.

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Vardasca, R., M. Clemente, A. Pinto, and J. Gabriel. "The outcomes of thermal symmetry after orofacial pain acupuncture treatment." In 2016 Quantitative InfraRed Thermography. QIRT Council, 2016. http://dx.doi.org/10.21611/qirt.2016.143.

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Wu, Ke, and Weiyang Chen. "Quantitative Analysis of Facial Symmetry Among Different Expressions." In 2021 7th International Conference on Systems and Informatics (ICSAI). IEEE, 2021. http://dx.doi.org/10.1109/icsai53574.2021.9664110.

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Cirett-Galán, Federico, Raquel Torres-Peralta, Valery Chernov, Grigory Chernov, José Luis Ruiz-Duarte, and Marcelino Barboza-Flores. "Using Breast Contour to Generate a Measure of Shape and Size Symmetry." In Quantitative InfraRed Thermography Asia 2015. QIRT Council, 2015. http://dx.doi.org/10.21611/qirt.2015.0080.

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Ponti, S. "Ultrasonic wave propagation in stratified media with helical symmetry." In 26th Annual review of progress in quantitative nondestrictive evaluation. AIP, 2000. http://dx.doi.org/10.1063/1.1306049.

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Donaldson, Alastair F., Alice Miller, and David Parker. "Language-Level Symmetry Reduction for Probabilistic Model Checking." In 2009 Sixth International Conference on the Quantitative Evaluation of Systems (QEST). IEEE, 2009. http://dx.doi.org/10.1109/qest.2009.21.

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Azcoiti, V., V. Laliena, and X. Q. Luo. "NEW WAY FOR A QUANTITATIVE UNDERSTANDING OF CHIRAL-SYMMETRY BREAKING." In Proceedings of the International RCNP Workshop. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814447140_0044.

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Livings, R. A., V. Dayal, D. J. Barnard, and D. K. Hsu. "Limitations of symmetry in FE modeling: A comparison of fem and air-coupled resonance imaging." In REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: Volume 31. AIP, 2012. http://dx.doi.org/10.1063/1.4716432.

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Neubeckcr, R., and T. Tschudi. "Analysis of optical pattern formation by symmetry autocorrelation functions." In The European Conference on Lasers and Electro-Optics. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/cleo_europe.1996.cmj4.

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Today, spontaneous pattern formation is a phenomenon observed in a wide spectrum of nonlinear optical systems [1,2]. Still, the systematic analysis of such patterns is a problem, because of the lack of general characterization algorithms, allowing a quantitative evaluation of the patterns’s complexity.
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Korčáková, Daniela, Viktor Votruba, Jiří Kubát, Klaus Werner, Petr Škoda, Thorsten Nagel, Ivan Hubeny, James M. Stone, Keith MacGregor, and Klaus Werner. "Radiative Transfer in Axial Symmetry." In RECENT DIRECTIONS IN ASTROPHYSICAL QUANTITATIVE SPECTROSCOPY AND RADIATION HYDRODYNAMICS: Proceedings of the International Conference in Honor of Dimitri Mihalas for His Lifetime Scientific Contributions on the Occasion of His 70th Birthday. AIP, 2009. http://dx.doi.org/10.1063/1.3250083.

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Reports on the topic "Quantitative symmetry"

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Hart, Carl R., and Gregory W. Lyons. A Measurement System for the Study of Nonlinear Propagation Through Arrays of Scatterers. Engineer Research and Development Center (U.S.), November 2020. http://dx.doi.org/10.21079/11681/38621.

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Abstract:
Various experimental challenges exist in measuring the spatial and temporal field of a nonlinear acoustic pulse propagating through an array of scatterers. Probe interference and undesirable high-frequency response plague typical approaches with acoustic microphones, which are also limited to resolving the pressure field at a single position. Measurements made with optical methods do not have such drawbacks, and schlieren measurements are particularly well suited to measuring both the spatial and temporal evolution of nonlinear pulse propagation in an array of scatterers. Herein, a measurement system is described based on a z-type schlieren setup, which is suitable for measuring axisymmetric phenomena and visualizing weak shock propagation. In order to reduce directivity and initiate nearly spherically-symmetric propagation, laser induced breakdown serves as the source for the nonlinear pulse. A key component of the schlieren system is a standard schliere, which allows quantitative schlieren measurements to be performed. Sizing of the standard schliere is aided by generating estimates of the expected light refraction from the nonlinear pulse, by way of the forward Abel transform. Finally, considerations for experimental sequencing, image capture, and a reconfigurable rod array designed to minimize spurious wave interactions are specified. 15.
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