24,571 research outputs found
The linearization problem of a binary quadratic problem and its applications
We provide several applications of the linearization problem of a binary
quadratic problem. We propose a new lower bounding strategy, called the
linearization-based scheme, that is based on a simple certificate for a
quadratic function to be non-negative on the feasible set. Each
linearization-based bound requires a set of linearizable matrices as an input.
We prove that the Generalized Gilmore-Lawler bounding scheme for binary
quadratic problems provides linearization-based bounds. Moreover, we show that
the bound obtained from the first level reformulation linearization technique
is also a type of linearization-based bound, which enables us to provide a
comparison among mentioned bounds. However, the strongest linearization-based
bound is the one that uses the full characterization of the set of linearizable
matrices. Finally, we present a polynomial-time algorithm for the linearization
problem of the quadratic shortest path problem on directed acyclic graphs. Our
algorithm gives a complete characterization of the set of linearizable matrices
for the quadratic shortest path problem
Topological Phases in the Single-Layer FeSe
A distinct electronic structure was observed in the single-layer FeSe which
shows surprising high temperature superconductivity over 65k. Here we
demonstrate that the electronic structure can be explained by the strain effect
due to substrates. More importantly, we find that this electronic structure can
be tuned into robust topological phases from a topologically trivial metallic
phase by the spin-orbital interaction and couplings to substrates. The
topological phase is robust against any perturbations that preserve the
time-reversal symmetry. Our studies suggest that topological phases and
topologically related properties such as Majorana Fermions can be realized in
iron-based high T superconductors.Comment: 9 pages, 5 figue
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