47,427 research outputs found
Blind Two-Dimensional Super-Resolution and Its Performance Guarantee
In this work, we study the problem of identifying the parameters of a linear
system from its response to multiple unknown input waveforms. We assume that
the system response, which is the only given information, is a scaled
superposition of time-delayed and frequency-shifted versions of the unknown
waveforms. Such kind of problem is severely ill-posed and does not yield a
unique solution without introducing further constraints. To fully characterize
the linear system, we assume that the unknown waveforms lie in a common known
low-dimensional subspace that satisfies certain randomness and concentration
properties. Then, we develop a blind two-dimensional (2D) super-resolution
framework that applies to a large number of applications such as radar imaging,
image restoration, and indoor source localization. In this framework, we show
that under a minimum separation condition between the time-frequency shifts,
all the unknowns that characterize the linear system can be recovered precisely
and with very high probability provided that a lower bound on the total number
of the observed samples is satisfied. The proposed framework is based on 2D
atomic norm minimization problem which is shown to be reformulated and solved
efficiently via semidefinite programming. Simulation results that confirm the
theoretical findings of the paper are provided
Convergence of Gradient Descent for Low-Rank Matrix Approximation
This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny-Study distance on this space
Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators
The ground state of translationally-invariant insulators comprise bands which
can assume topologically distinct structures. There are few known examples
where this distinction is enforced by a point-group symmetry alone. In this
paper we show that 1D and 2D insulators with the simplest point-group symmetry
- inversion - have a classification. In 2D, we identify a relative
winding number that is solely protected by inversion symmetry. By analysis of
Berry phases, we show that this invariant has similarities with the first Chern
class (of time-reversal breaking insulators), but is more closely analogous to
the invariant (of time-reversal invariant insulators). Implications of
our work are discussed in holonomy, the geometric-phase theory of polarization,
the theory of maximally-localized Wannier functions, and in the entanglement
spectrum.Comment: The updated version is accepted in Physical Review
Pseudogap and incommensurate magnetic fluctuations in YBa_2Cu_3O_{6. 6}
Unpolarized inelastic neutron scattering is used to study the temperature and
wave vector dependence of the dynamical magnetic susceptibility,
, of a well characterized single crystal
( K). We find that a pseudogap opens in the spin fluctuation spectrum
at temperatures well above . We speculate that the appearance of the low
frequency incommensurate fluctuations is associated with the opening of the
pseudogap. To within the error of the measurements, a gap in the spin
fluctuation spectrum is found in the superconducting state.Comment: 6 pages, 3 ps figs, Proceedings of ICNS, Physica B, to be publishe
Observation of Magnetic Moments in the Superconducting State of YBaCuO
Neutron Scattering measurements for YBaCuO have identified
small magnetic moments that increase in strength as the temperature is reduced
below and further increase below . An analysis of the data shows
the moments are antiferromagnetic between the Cu-O planes with a correlation
length of longer than 195 \AA in the - plane and about 35 \AA along the
c-axis. The origin of the moments is unknown, and their properties are
discusssed both in terms of Cu spin magnetism and orbital bond currents.Comment: 9 pages, and 4 figure
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