2,513 research outputs found
Changes of Kondo effect in the junction with DIII-class topological and -wave superconductors
We discuss the change of the Kondo effect in the Josephson junction formed by
the indirect coupling between a one-dimensional \emph{DIII}-class topological
and s-wave superconductors via a quantum dot. By performing the
Schrieffer-Wolff transformation, we find that the single-electron occupation in
the quantum dot induces various correlation modes, such as the Kondo and
singlet-triplet correlations between the quantum dot and the -wave
superconductor and the spin exchange correlation between the dot and Majorana
doublet. Moreover, it plays a nontrivial role in modifying the Josephson
effect, leading to the occurrence of anisotropic and high-order Kondo
correlation. In addition, due to the quantum dot in the Kondo regime, extra
spin exchange correlations contribute to the Josephson effect as well.
Nevertheless, if the \emph{DIII}-class topological superconductor degenerates
into \emph{D}-class because of the destruction of time-reversal invariance, all
such terms will disappear completely. We believe that this work shows the
fundamental difference between the \emph{D}- and \emph{DIII}-class topological
superconductors.Comment: 10 pages, 3 figures. Any comment is welcom
Semantic Graph for Zero-Shot Learning
Zero-shot learning aims to classify visual objects without any training data
via knowledge transfer between seen and unseen classes. This is typically
achieved by exploring a semantic embedding space where the seen and unseen
classes can be related. Previous works differ in what embedding space is used
and how different classes and a test image can be related. In this paper, we
utilize the annotation-free semantic word space for the former and focus on
solving the latter issue of modeling relatedness. Specifically, in contrast to
previous work which ignores the semantic relationships between seen classes and
focus merely on those between seen and unseen classes, in this paper a novel
approach based on a semantic graph is proposed to represent the relationships
between all the seen and unseen class in a semantic word space. Based on this
semantic graph, we design a special absorbing Markov chain process, in which
each unseen class is viewed as an absorbing state. After incorporating one test
image into the semantic graph, the absorbing probabilities from the test data
to each unseen class can be effectively computed; and zero-shot classification
can be achieved by finding the class label with the highest absorbing
probability. The proposed model has a closed-form solution which is linear with
respect to the number of test images. We demonstrate the effectiveness and
computational efficiency of the proposed method over the state-of-the-arts on
the AwA (animals with attributes) dataset.Comment: 9 pages, 5 figure
Nonlocal theory solution of two collinear cracks in the functionally graded materials
AbstractIn this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials
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