Recently, some authors proposed the use of symmetric weightsfor computing the elements of cross-efficiency matrix. In spite ofthe fact that the proposed method decreases the number of zeroweights, a large number of zero weights may still exist among inputand output symmetric weights. To decrease the number of input andoutput symmetric weights, this paper improves the proposed secondarygoal mode...

An Au-SiO2-Au (metal-insulator-metal; MIM) surface-plasmon-polariton (SPP) guide is schematically presented in Fig. S1a. As the name “MIM” implies, a structural symmetry exists with respect to the mirror plane that cuts through the center of the SiO2 layer and is parallel to the x–y plane. As a result, supported SPP modes in the guide can be classified into two major types, each with its own di...

Human faces are approximately bilaterally symmetric. We study the ability to generalize to novel views of human faces focusing on the role of that symmetry. Our hypothesis is that the ability to identify mirror symmetric images is used for viewpoint generalization by approximating the symmetric view of a learned view by its mirror symmetric image. Two psychophysical experiments are performed us...

We address the problem of 3-D reconstruction from a single perspective view of a mirror symmetric scene. We establish the fundamental result that it is geometrically equivalent to observing the scene with two cameras, the cameras being symmetrical with respect to the unknown 3-D symmetry plane. All traditional tools of classical 2-view stereo can then be applied, and the concepts of fundamen-ta...

We address the problem of 3-D reconstruction from a single perspective view of a mirror symmetric scene. We establish the fundamental result that it is geometrically equivalent to observing the scene with two cameras, the cameras being symmetrical with respect to the unknown 3-D symmetry plane. All traditional tools of classical 2-view stereo can then be applied, and the concepts of fundamental...

In this paper, we show that a matrix A in Mn(C) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. And also show that if allconeigenvalues of conjugate-normal matrix A be real, then it is symmetric.  

Integrated circulators and isolators are important for developing on-chip optical technologies, such as laser cavities, communication systems, quantum information processors. These devices appear to inherently require mirror symmetry breaking separate backwards from forwards propagation, so existing implementations rely upon magnetic materials, or interactions driven by propagating waves. In co...