3,055 research outputs found
Quantitative gradient estimates for harmonic maps into singular spaces
In this paper, we will show the Yau's gradient estimate for harmonic maps
into a metric space with curvature bounded above by a constant
, , in the sense of Alexandrov. As a direct application,
it gives some Liouville theorems for such harmonic maps. This extends the works
of S. Y. Cheng [4] and H. I. Choi [5] to harmonic maps into singular spaces.Comment: The main results in the first version have been improved. To appear
in SCIENCE CHINA Mathematic
Segment-Sliding Reconstruction of Pulsed Radar Echoes with Sub-Nyquist Sampling
It has been shown that analog-to-information con- version (AIC) is an
efficient scheme to perform sub-Nyquist sampling of pulsed radar echoes.
However, it is often impractical, if not infeasible, to reconstruct full-range
Nyquist samples because of huge storage and computational load requirements.
Based on the analyses of AIC measurement system, this paper develops a novel
segment-sliding reconstruction (SegSR) scheme to effectively reconstruct the
Nyquist samples. The SegSR per- forms segment-by-segment reconstruction in a
sliding mode and can be implemented in real-time. An important characteristic
that distinguish the proposed SegSR from the existing methods is that the
measurement matrix in each segment satisfies the restricted isometry property
(RIP) condition. Partial support in the previous segment can be incorporated
into the estimation of the Nyquist samples in the current segment. The effect
of interference intro- duced from adjacent segments is theoretically analyzed,
and it is revealed that the interference consists of two interference levels
having different impacts to the signal reconstruction performance. With these
observations, a two-step orthogonal matching pursuit (OMP) procedure is
proposed for segment reconstruction, which takes into account different
interference levels and partially known support of the previous segment. The
proposed SegSR achieves nearly optimal reconstruction performance with a signi-
ficant reduction of computational loads and storage requirements. Theoretical
analyses and simulations verify its effectiveness.Comment: 13 pages, 10 figure
Gridless Quadrature Compressive Sampling with Interpolated Array Technique
Quadrature compressive sampling (QuadCS) is a sub-Nyquist sampling scheme for
acquiring in-phase and quadrature (I/Q) components in radar. In this scheme,
the received intermediate frequency (IF) signals are expressed as a linear
combination of time-delayed and scaled replicas of the transmitted waveforms.
For sparse IF signals on discrete grids of time-delay space, the QuadCS can
efficiently reconstruct the I/Q components from sub-Nyquist samples. In
practice, the signals are characterized by a set of unknown time-delay
parameters in a continuous space. Then conventional sparse signal
reconstruction will deteriorate the QuadCS reconstruction performance. This
paper focuses on the reconstruction of the I/Q components with continuous delay
parameters. A parametric spectrum-matched dictionary is defined, which sparsely
describes the IF signals in the frequency domain by delay parameters and gain
coefficients, and the QuadCS system is reexamined under the new dictionary.
With the inherent structure of the QuadCS system, it is found that the
estimation of delay parameters can be decoupled from that of sparse gain
coefficients, yielding a beamspace direction-of-arrival (DOA) estimation
formulation with a time-varying beamforming matrix. Then an interpolated
beamspace DOA method is developed to perform the DOA estimation. An optimal
interpolated array is established and sufficient conditions to guarantee the
successful estimation of the delay parameters are derived. With the estimated
delays, the gain coefficients can be conveniently determined by solving a
linear least-squares problem. Extensive simulations demonstrate the superior
performance of the proposed algorithm in reconstructing the sparse signals with
continuous delay parameters.Comment: 34 pages, 11 figure
Quantized Anomalous Hall Effect in Magnetic Topological Insulators
The Hall effect, the anomalous Hall effect and the spin Hall effect are
fundamental transport processes in solids arising from the Lorentz force and
the spin-orbit coupling respectively. The quantum versions of the Hall effect
and the spin Hall effect have been discovered in recent years. However, the
quantized anomalous Hall (QAH) effect has not yet been realized experimentally.
In a QAH insulator, spontaneous magnetic moments and spin-orbit coupling
combine to give rise to a topologically non-trivial electronic structure,
leading to the quantized Hall effect without any external magnetic field. In
this work, based on state-of-art first principles calculations, we predict that
the tetradymite semiconductors BiTe, BiSe, and SbTe
form magnetically ordered insulators when doped with transition metal elements
(Cr or Fe), in sharp contrast to conventional dilute magnetic semiconductor
where free carriers are necessary to mediate the magnetic coupling. Magnetic
order in two-dimensional thin films gives rise to a topological electronic
structure characterized by a finite Chern number, with quantized Hall
conductance . Experimental realization of the long sought-after QAH
insulator state could enable robust dissipationless charge transport at room
temperature.Comment: 19 pages, 5 figure
Coherent-feedback-induced photon blockade and optical bistability by an optomechanical controller
It is well-known that some nonlinear phenomena such as strong photon blockade
are hard to be observed in optomechanical system with current experimental
technology. Here, we present a coherent feedback control strategy in which a
linear cavity is coherently controlled by an optomechanical controller in a
feedback manner. The coherent feedback loop transfers and enhances quantum
nonlinearity from the controller to the controlled cavity, which makes it
possible to observe strong nonlinear effects in either linear cavity or
optomechanical cavity. More interestingly, we find that the strong photon
blockade under single-photon optomechanical weak coupling condition could be
observed in the quantum regime. Additionally, the coherent feedback loop leads
to two-photon and multiphoton tunnelings for the controlled linear cavity,
which are also typical quantum nonlinear phenomenon. We hope that our work can
give new perspectives in engineering nonlinear quantum phenomena.Comment: 12 pages, 11 figure
Predicted alternative structure for tantalum metal under high pressure and high temperature
First-principles simulations have been performed to investigate the phase
stability of tantalum metal under high pressure and high temperature (HPHT). We
searched its low-energy structures globally using our developed multi-algorithm
collaborative (MAC) crystal structure prediction technique. The body-centred
cubic (bcc) was found to be stable at pressure up to 300 GPa. The previously
reported and \textit{A}15 structures were also reproduced
successfully. More interestingly, we observed another phase (space group:
\textit{Pnma}, 62) that is more stable than and \textit{A}15. Its
stability is confirmed by its phonon spectra and elastic constants. For
-Ta, the calculated elastic constants and high-temperature phonon
spectra both imply that it is neither mechanically nor dynamically stable.
Thus, is not the structure to which bcc-Ta transits before melting. On
the contrary, the good agreement of \textit{Pnma}-Ta shear sound velocities
with experiment suggests \textit{Pnma} is the new structure of Ta implied by
the discontinuation of shear sound velocities in recent shock experiment [J.
Appl. Phys. \textbf{111}, 033511 (2012)]
Isospin dependence of incompressibility in relativistic and non-relativistic mean field calculations
The isospin dependence of incompressibility is investigated in the Skyrme
Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations
between the nuclear matter incompressibility and the isospin dependent term of
the finite nucleus incompressibility is elucidated by using the Thomas-Fermi
approximation. The Coulomb term is also studied by using various different
Skyrme
Hamiltonians and RMF Lagrangians. The symmetry energy coefficient of
incompressibility is extracted to be K_{\tau}=-(500\pm50) MeV from the recent
experimental data of isoscalar giant monopole resonances (ISGMR) in Sn
isotopes. Microscopic HF+random phase approximation (RPA) calculations are also
performed with Skyrme interactions for ^{208}Pb and Sn isotopes to study the
strength distributions of ISGMR. .Comment: 19pages,5figure
Path-averaged Kinetic Equation for Stochastic Systems
For a stochastic system, its evolution from one state to another can have a
large number of possible paths. Non-uniformity in the field of system variables
leads the local dynamics in state transition varies considerably from path to
path and thus the distribution of the paths affects statistical characteristics
of the system. Such a characteristic can be referred to as path-dependence of a
system, and long-time correlation is an intrinsic feature of path-dependence
systems. We employed a local path density operator to describe the distribution
of state transition paths, and based on which we derived a new kinetic equation
for path-dependent systems. The kinetic equation is similar in form to the
Kramers-Moyal expansion, but with its expansion coefficients determined by the
cumulants with respect to state transition paths, instead of transition
moments. This characteristic makes it capable of accounting for the non-local
feature of systems, which is essential in studies of large scale systems where
the path-dependence is prominent. Short-time correlation approximation is also
discussed. It shows that the cumulants of state transition paths are equivalent
to jump moments when correlation time scales are infinitesimal, as makes the
kinetic equation derived in this paper has the same physical consideration of
the Fokker-Planck equation for Markov processes.Comment: re-written the formulatio
Transductive Zero-Shot Learning with a Self-training dictionary approach
As an important and challenging problem in computer vision, zero-shot
learning (ZSL) aims at automatically recognizing the instances from unseen
object classes without training data. To address this problem, ZSL is usually
carried out in the following two aspects: 1) capturing the domain distribution
connections between seen classes data and unseen classes data; and 2) modeling
the semantic interactions between the image feature space and the label
embedding space. Motivated by these observations, we propose a bidirectional
mapping based semantic relationship modeling scheme that seeks for crossmodal
knowledge transfer by simultaneously projecting the image features and label
embeddings into a common latent space. Namely, we have a bidirectional
connection relationship that takes place from the image feature space to the
latent space as well as from the label embedding space to the latent space. To
deal with the domain shift problem, we further present a transductive learning
approach that formulates the class prediction problem in an iterative refining
process, where the object classification capacity is progressively reinforced
through bootstrapping-based model updating over highly reliable instances.
Experimental results on three benchmark datasets (AwA, CUB and SUN) demonstrate
the effectiveness of the proposed approach against the state-of-the-art
approaches
Oscillatory crossover from two dimensional to three dimensional topological insulators
We investigate the crossover regime from three dimensional topological
insulators and to two dimensional topological insulators
with quantum spin Hall effect when the layer thickness is reduced. Using both
analytical models and first-principles calculations, we find that the crossover
occurs in an oscillatory fashion as a function of the layer thickness,
alternating between topologically trivial and non-trivial two dimensional
behavior.Comment: 5 pages, 3 figures; 3 added references, an added not
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