Topic
Antisymmetry
About: Antisymmetry is a research topic. Over the lifetime, 214 publications have been published within this topic receiving 7914 citations.
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05 Sep 2010
TL;DR: This paper proposes a novel approach to segment three dimensional curvilinear structures, particularly vessels in angiography, by inspecting the symmetry of image gradients by exploiting the symmetric image gradient pattern observed at structure centers.
Abstract: This paper proposes a novel approach to segment three dimensional curvilinear structures, particularly vessels in angiography, by inspecting the symmetry of image gradients. The proposed method stresses the importance of simultaneously considering both the gradient symmetry with respect to the curvilinear structure center, and the gradient antisymmetry with respect to the object boundary. Measuring the image gradient symmetry remarkably suppresses the disturbance introduced by rapid intensity changes along curvilinear structures. Meanwhile, considering the image gradient antisymmetry helps locate the structure boundary. The gradient symmetry and the gradient antisymmetry are evaluated based on the notion of oriented flux. By utilizing the aforementioned gradient symmetry information, an active contour model is tailored to perform segmentation. On the one hand, by exploiting the symmetric image gradient pattern observed at structure centers, the contours expand along curvilinear structures even through there exists intensity fluctuation along the structures. On the other hand, measuring the antisymmetry of the image gradient conveys strong detection responses to precisely drive contours to the structure boundaries, as well as avoiding contour leakages. The proposed method is capable of delivering promising segmentation results. This is validated in the experiments using synthetic data and real vascular images of different modalities, and through the comparison to two well founded and published methods for curvilinear structure segmentation.
46 citations
TL;DR: In this article, it was shown that the transmission eigenvalues of the scattering matrix come in pairs in time reversal symmetric systems with half integral spins, which is valid both for even and odd number of modes and relies solely on the antisymmetry imposed by time reversal symmetry.
Abstract: In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.
45 citations
TL;DR: It is suggested that movement is a symmetry-breaking phenomenon, i.e. it is triggered by purely geometrical factors as opposed to morphological ones.
Abstract: Movement is a specific property of human languages and one that has at least implicitly been recognized in all linguistic theories. The most recent development posits that movement is forced by morphological requirements (Chomsky 1995). In this paper I will suggest a different approach to movement, suggesting that it is essentially related to the geometry of phrase structure. A weak version of Kayne's 1994 theory of the antisymmetry of syntax, namely 'dynamic antisymmetry' will be introduced. In the strong version, UG only allowed for antisymmetrical configurations, in terms of c-command. Within dynamic antisymmetry, however, symmetrical configurations can be generated, provided that movement makes them antisymmetric before spell-out. In other words, I will suggest that movement is a symmetry-breaking phenomenon, i.e. it is triggered by purely geometrical factors as opposed to morphological ones. Data will range from small clause constructions (both in copular sentences and believe-type verbs) to wh-movement in interrogatives. Italian and English will be the major sources of examples.
45 citations
05 Feb 2020
TL;DR: In this paper, higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified.
Abstract: Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a space-time symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the K groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective.
42 citations