34,506 research outputs found
Large Scale Structure Formation of Normal Branch in DGP Brane World Model
In this paper, we study the large scale structure formation of the normal
branch in DGP model (Dvail, Gabadadze and Porrati brane world model) by
applying the scaling method developed by Sawicki, Song and Hu for solving the
coupled perturbed equations of motion of on-brane and off-brane. There is
detectable departure of perturbed gravitational potential from LCDM even at the
minimal deviation of the effective equation of state w_eff below -1. The
modified perturbed gravitational potential weakens the integrated Sachs-Wolfe
effect which is strengthened in the self-accelerating branch DGP model.
Additionally, we discuss the validity of the scaling solution in the de Sitter
limit at late times.Comment: 6 pages, 2 figure
Violation of monogamy inequality for higher-dimensional objects
Bipartite quantum entanglement for qutrits and higher-dimensional objects is
considered. We analyze the possibility of violation of monogamy inequality,
introduced by Coffman, Kundu, and Wootters, for some systems composed of such
objects. An explicit counterexample with a three-qutrit totally antisymmetric
state is presented. Since three-tangle has been confirmed to be a natural
measure of entanglement for qubit systems, our result shows that the
three-tangle is no longer a legitimate measure of entanglement for states with
three qutrits or higher dimensional objects.Comment: 2.5 pages,minor modifications are mad
Convolutional Dictionary Learning: Acceleration and Convergence
Convolutional dictionary learning (CDL or sparsifying CDL) has many
applications in image processing and computer vision. There has been growing
interest in developing efficient algorithms for CDL, mostly relying on the
augmented Lagrangian (AL) method or the variant alternating direction method of
multipliers (ADMM). When their parameters are properly tuned, AL methods have
shown fast convergence in CDL. However, the parameter tuning process is not
trivial due to its data dependence and, in practice, the convergence of AL
methods depends on the AL parameters for nonconvex CDL problems. To moderate
these problems, this paper proposes a new practically feasible and convergent
Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The
BPG-M-based CDL is investigated with different block updating schemes and
majorization matrix designs, and further accelerated by incorporating some
momentum coefficient formulas and restarting techniques. All of the methods
investigated incorporate a boundary artifacts removal (or, more generally,
sampling) operator in the learning model. Numerical experiments show that,
without needing any parameter tuning process, the proposed BPG-M approach
converges more stably to desirable solutions of lower objective values than the
existing state-of-the-art ADMM algorithm and its memory-efficient variant do.
Compared to the ADMM approaches, the BPG-M method using a multi-block updating
scheme is particularly useful in single-threaded CDL algorithm handling large
datasets, due to its lower memory requirement and no polynomial computational
complexity. Image denoising experiments show that, for relatively strong
additive white Gaussian noise, the filters learned by BPG-M-based CDL
outperform those trained by the ADMM approach.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Image
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