9,688 research outputs found
The tensor renormalization group study of the general spin-S Blume-Capel model
We focus on the special situation of of the general spin-S Blume-Capel
model on the square lattice. Under the infinitesimal external magnetic field,
the phase transition behaviors due to the thermal fluctuations are discussed by
the newly developed tensor renormalization group method. For the case of the
integer spin-S, the system will undergo first-order phase transitions with
the successive symmetry breaking with the magnetization . For the
half-integer spin-S, there are similar first order phase transition
with stepwise structure, in addition, there is a continuous
phase transition due to the spin-flip symmetry breaking. In the low
temperature regions, all first-order phase transitions are accompanied by the
successive disappearance of the optional spin-component pairs(),
furthermore, the critical temperature for the nth first-order phase transition
is the same, independent of the value of the spin-S. In the absence of the
magnetic field, the visualization parameter characterizing the intrinsic
degeneracy of the different phases clearly demonstrates the phase transition
process.Comment: 6 pages, 7 figure
On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices
This letter is on the performance of the turbo signal recovery (TSR)
algorithm for partial discrete Fourier transform (DFT) matrices based
compressed sensing. Based on state evolution analysis, we prove that TSR with a
partial DFT sensing matrix outperforms the well-known approximate message
passing (AMP) algorithm with an independent identically distributed (IID)
sensing matrix.Comment: to appear in IEEE Signal Processing Letter
Lyapunov Functions in Piecewise Linear Systems: From Fixed Point to Limit Cycle
This paper provides a first example of constructing Lyapunov functions in a
class of piecewise linear systems with limit cycles. The method of construction
helps analyze and control complex oscillating systems through novel geometric
means. Special attention is stressed upon a problem not formerly solved: to
impose consistent boundary conditions on the Lyapunov function in each linear
region. By successfully solving the problem, the authors construct continuous
Lyapunov functions in the whole state space. It is further demonstrated that
the Lyapunov functions constructed explain for the different bifurcations
leading to the emergence of limit cycle oscillation
Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure
for finding sparse solutions of underdetermined linear systems. This method has
been shown to have strong theoretical guarantee and impressive numerical
performance. In this paper, we generalize HTP from compressive sensing to a
generic problem setup of sparsity-constrained convex optimization. The proposed
algorithm iterates between a standard gradient descent step and a hard
thresholding step with or without debiasing. We prove that our method enjoys
the strong guarantees analogous to HTP in terms of rate of convergence and
parameter estimation accuracy. Numerical evidences show that our method is
superior to the state-of-the-art greedy selection methods in sparse logistic
regression and sparse precision matrix estimation tasks
Cycle-SUM: Cycle-consistent Adversarial LSTM Networks for Unsupervised Video Summarization
In this paper, we present a novel unsupervised video summarization model that
requires no manual annotation. The proposed model termed Cycle-SUM adopts a new
cycle-consistent adversarial LSTM architecture that can effectively maximize
the information preserving and compactness of the summary video. It consists of
a frame selector and a cycle-consistent learning based evaluator. The selector
is a bi-direction LSTM network that learns video representations that embed the
long-range relationships among video frames. The evaluator defines a learnable
information preserving metric between original video and summary video and
"supervises" the selector to identify the most informative frames to form the
summary video. In particular, the evaluator is composed of two generative
adversarial networks (GANs), in which the forward GAN is learned to reconstruct
original video from summary video while the backward GAN learns to invert the
processing. The consistency between the output of such cycle learning is
adopted as the information preserving metric for video summarization. We
demonstrate the close relation between mutual information maximization and such
cycle learning procedure. Experiments on two video summarization benchmark
datasets validate the state-of-the-art performance and superiority of the
Cycle-SUM model over previous baselines.Comment: Accepted at AAAI 201
A magnetohydrodynamic model for multi-wavelength flares from Sagittarius~A (I): model and the near-infrared and X-ray flares
Flares from the supermassive black hole in our Galaxy, Sagittarius~A
(Sgr A), are routinely observed over the last decade or so. Despite
numerous observational and theoretical efforts, the nature of such flares still
remains poorly understood, although a few phenomenological scenarios have been
proposed. In this work, we develop the Yuan et al. (2009) scenario into a
magnetohydrodynamic (MHD) model for Sgr A flares. This model is
analogous with the theory of solar flares and coronal mass ejection in solar
physics. In the model, magnetic field loops emerge from the accretion flow onto
Sgr A and are twisted to form flux ropes because of shear and
turbulence. The magnetic energy is also accumulated in this process until a
threshold is reached. This then results in a catastrophic evolution of a flux
rope with the help of magnetic reconnection in the current sheet. In this
catastrophic process, the magnetic energy is partially converted into the
energy of non-thermal electrons. We have quantitatively calculated the
dynamical evolution of the height, size, and velocity of the flux rope, as well
as the magnetic field in the flare regions, and the energy distribution of
relativistic electrons in this process. We further calculate the synchrotron
radiation from these electrons and compare the obtained light curves with the
observed ones. We find that the model can reasonably explain the main
observations of near-infrared (NIR) and X-ray flares including their light
curves and spectra. It can also potentially explain the frequency-dependent
time delay seen in radio flare light curves.Comment: 17 pages, 13 figures, accepted by MNRA
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