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As one kind of mechanical static structure symmetry, glide symmetry is grouped by mirror symmetry and translation symmetry. Glide symmetry is widely exists in mechanical systems, and plays an important role in realizing the techni...
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As one kind of mechanical static structure symmetry, glide symmetry is grouped by mirror symmetry and translation symmetry. Glide symmetry is widely exists in mechanical systems, and plays an important role in realizing the technical, economic and social performances of mechanical products. On the basis of research on the concept systems of mirror symmetry, translation symmetry and glide symmetric instances, and taking the characters of the different combined types of symmetry benchmarks as the standard, the concept system of mechanical glide symmetry was established, which can be the foundation of further researches on the application laws of glide symmetry in mechanical systems.
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摘要 :
As one kind of mechanical static structure symmetry, glide symmetry is grouped by mirror symmetry and translation symmetry. Glide symmetry is widely exists in mechanical systems, and plays an important role in realizing the techni...
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As one kind of mechanical static structure symmetry, glide symmetry is grouped by mirror symmetry and translation symmetry. Glide symmetry is widely exists in mechanical systems, and plays an important role in realizing the technical, economic and social performances of mechanical products. On the basis of research on the concept systems of mirror symmetry, translation symmetry and glide symmetric instances, and taking the characters of the different combined types of symmetry benchmarks as the standard, the concept system of mechanical glide symmetry was established, which can be the foundation of further researches on the application laws of glide symmetry in mechanical systems.
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Many satisfiability problems exhibit symmetry properties. Thus, the development of symmetry exploitation techniques seems a natural way to try to improve the efficiency of solvers by preventing them from exploring isomorphic parts...
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Many satisfiability problems exhibit symmetry properties. Thus, the development of symmetry exploitation techniques seems a natural way to try to improve the efficiency of solvers by preventing them from exploring isomorphic parts of the search space. These techniques can be classified into two categories: dynamic and static symmetry breaking. Static approaches have often appeared to be more effective than dynamic ones. But although these approaches can be considered as complementary, very few works have tried to combine them. In this paper, we present a new tool, COSYSEL, that implements a composition of the static Effective Symmetry Breaking Predicates (ESBP) technique with the dynamic Symmetric Explanation Learning (SEL). ESBP exploits symmetries to prune the search tree and SEL uses symmetries to speed up the tree traversal. These two accelerations are complementary and their combination was made possible by the introduction of Local symmetries. We conduct our experiments on instances issued from the last ten SAT competitions and the results show that our tool outperforms the existing tools on highly symmetrical problems.
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The symmetry computation has recently been recognized as a topic of interest in many different fields of computer vision and image analysis, which still remains as an open problem. In this work we propose an unified method to comp...
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The symmetry computation has recently been recognized as a topic of interest in many different fields of computer vision and image analysis, which still remains as an open problem. In this work we propose an unified method to compute image symmetries based on finding the minimum-variance partitions of the image that best describe its repetitive nature. We then use a statistical measurement of these partitions as symmetry score. The principal idea is that the same measurement can be used to score symmetries (rotation, reflection, and glide reflection). Finally, a feature vector composed from these symmetry values is used to classify the whole image according to a symmetry group. An increase in the success rate, compared to other reference methods, indicates the improved discriminative capabilities of the proposed symmetry features. Our experimental results improve the state of the art in wallpaper classification methods.
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摘要 :
The symmetry computation has recently been recognized as a topic of interest in many different fields of computer vision and image analysis, which still remains as an open problem. In this work we propose an unified method to comp...
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The symmetry computation has recently been recognized as a topic of interest in many different fields of computer vision and image analysis, which still remains as an open problem. In this work we propose an unified method to compute image symmetries based on finding the minimum-variance partitions of the image that best describe its repetitive nature. We then use a statistical measurement of these partitions as symmetry score. The principal idea is that the same measurement can be used to score symmetries (rotation, reflection, and glide reflection). Finally, a feature vector composed from these symmetry values is used to classify the whole image according to a symmetry group. An increase in the success rate, compared to other reference methods, indicates the improved discriminative capabilities of the proposed symmetry features. Our experimental results improve the state of the art in wallpaper classification methods.
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The present paper analyses the mathematical concept of symmetry in the artwork of the Russian artist Kazimir Malevich. Symmetries are a perpetual presence in his entire artistic work, from the early stages, where Impressionism had...
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The present paper analyses the mathematical concept of symmetry in the artwork of the Russian artist Kazimir Malevich. Symmetries are a perpetual presence in his entire artistic work, from the early stages, where Impressionism had the first place, to the later paintings, which belong to Suprematism. The first part of the paper investigates the symmetry of the painting The athlete of the future, from 1913. The second part deals with the evolution of symmetry in three different paintings focusing on the same subject, which is three female figures. The paintings considered in this part can be reduced to a zero of forms - which is the essence of Suprematism - that possesses symmetry, and the paintings are analysed from this point of view.
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Scaling-rotation symmetry is combined by rotation symmetry and scaling symmetry, belongs to mechanical static structure symmetry, and widely exists in mechanical systems. Scaling-rotation symmetry plays an important role in realiz...
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Scaling-rotation symmetry is combined by rotation symmetry and scaling symmetry, belongs to mechanical static structure symmetry, and widely exists in mechanical systems. Scaling-rotation symmetry plays an important role in realizing the technical, economic and social performances of mechanical products. Based on the concept system of rotation symmetry and the research on large numbers of instances, taking the directivity, the rotary type and the alternations of symmetry components, the types of symmetry benchmark, and the variable type of scaling as standards, the concept system of scaling-rotation symmetry was established. The concept system can provide a theoretical basis for the further research on the application of scaling-rotation symmetry in mechanical systems.
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摘要 :
Scaling-rotation symmetry is combined by rotation symmetry and scaling symmetry, belongs to mechanical static structure symmetry, and widely exists in mechanical systems. Scaling-rotation symmetry plays an important role in re...
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Scaling-rotation symmetry is combined by rotation symmetry and scaling symmetry, belongs to mechanical static structure symmetry, and widely exists in mechanical systems. Scaling-rotation symmetry plays an important role in realizing the technical, economic and social performances of mechanical products. Based on the concept system of rotation symmetry and the research on large numbers of instances, taking the directivity, the rotary type and the alternations of symmetry components, the types of symmetry benchmark, and the variable type of scaling as standards, the concept system of scalingrotation symmetry was established. The concept system can provide a theoretical basis for the further research on the application of scaling-rotation symmetry in mechanical systems.
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This article proposes a new method for detecting symmetry points in images. Like other symmetry detection algorithms, it assigns a "symmetry score" to each image point. Our symmetry measure is only based on scalar products between...
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This article proposes a new method for detecting symmetry points in images. Like other symmetry detection algorithms, it assigns a "symmetry score" to each image point. Our symmetry measure is only based on scalar products between gradients and is therefore both easy to implement and of low runtime complexity. Moreover, our approach also yields the size of the symmetry region without additional computational effort. As both axial symmetries as well as some rotational symmetries can result in a point symmetry, we propose and evaluate different methods for identifying the rotational symmetries. We evaluate our method on two different test sets of real world images and compare it to several other rotational symmetry detection methods.
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We describe all symmetries of a single-input nonlinear control system, that is not feedback linearizable and whose first order approximation is controllable, around an equilibrium point. For a system such that a feedback transform...
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We describe all symmetries of a single-input nonlinear control system, that is not feedback linearizable and whose first order approximation is controllable, around an equilibrium point. For a system such that a feedback transformation, bringing it to the canonical form, is analytic we prove that the set of all local symmetries of the system is exhausted by exactly two 1-parameter families of symmetries, if the system is odd, and by exactly one 1-parameter family otherwise. We also prove that the form of the set of symmetries is completely described by the canonical form of the system: possessing a nonstationary symmetry, a 1-parameter family of symmetries, or being odd corresponds, respectively, to the fact that the drift vector field of the canonical form is periodic, does not depend on the first variable, or is odd. If the feedback transformation bringing the system to its canonical form is formal, we show an analogous result for an infinitesimal symmetry: its existence is equivalent to the fact that the drift vector field of the formal canonical form does not depend on the first variable. We illustrate our results by studying symmetries of the variable length pendulum.
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