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Controllable Goos-H\"{a}nchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field
The quantum Goos-H\"{a}nchen shift for ballistic electrons is investigated in
a parabolic potential well under a uniform vertical magnetic field. It is found
that the Goos-H\"{a}nchen shift can be negative as well as positive, and
becomes zero at transmission resonances. The beam shift depends not only on the
incident energy and incidence angle, but also on the magnetic field and Landau
quantum number. Based on these phenomena, we propose an alternative way to
realize the spin beam splitter in the proposed spintronic device, which can
completely separate spin-up and spin-down electron beams by negative and
positive Goos-H\"{a}nchen shifts.Comment: 6 pages, 6 figure
Hyperbolic Interaction Model For Hierarchical Multi-Label Classification
Different from the traditional classification tasks which assume mutual
exclusion of labels, hierarchical multi-label classification (HMLC) aims to
assign multiple labels to every instance with the labels organized under
hierarchical relations. Besides the labels, since linguistic ontologies are
intrinsic hierarchies, the conceptual relations between words can also form
hierarchical structures. Thus it can be a challenge to learn mappings from word
hierarchies to label hierarchies. We propose to model the word and label
hierarchies by embedding them jointly in the hyperbolic space. The main reason
is that the tree-likeness of the hyperbolic space matches the complexity of
symbolic data with hierarchical structures. A new Hyperbolic Interaction Model
(HyperIM) is designed to learn the label-aware document representations and
make predictions for HMLC. Extensive experiments are conducted on three
benchmark datasets. The results have demonstrated that the new model can
realistically capture the complex data structures and further improve the
performance for HMLC comparing with the state-of-the-art methods. To facilitate
future research, our code is publicly available
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