Tensor stability in Born-Infeld determinantal gravity

We consider the transverse-traceless tensor perturbation of a spatial flat homogeneous and isotropic spacetime in Born-Infeld determinantal gravity, and investigate the evolution of the tensor mode for two solutions in the early universe. For the first solution where the initial singularity is replaced by a regular geometric de Sitter inflation of infinite duration, the evolution of the tensor mode is stable for the parameter spaces $\alpha<-1$, $\omega\geq-1/3$ and $\alpha=-1$, $\omega>0$. For the second solution where the initial singularity is replaced by a primordial brusque bounce, which suffers a sudden singularity at the bouncing point, the evolution of the tensor mode is stable for all regions of the parameter space. Our calculation suggests that the tensor evolution can hold stability in large parameter spaces, which is a remarkable property of Born-Infeld determinantal gravity. We also constrain the theoretical parameter $|\lambda|\geq 10^{-38} \text{m}^{-2}$ by resorting to the current bound on the speed of the gravitational waves.Comment: 14 pages, added a general discussion on the tensor stability in Sec. 3, and added Sec. 5 on the parameter constraint, published versio

Brane worlds in gravity with auxiliary fields

Recently, Pani, Sotiriou, and Vernieri explored a new theory of gravity by adding nondynamical fields, i.e., gravity with auxiliary fields [Phys. Rev. D 88, 121502(R) (2013)]. In this gravity theory, higher-order derivatives of matter fields generically appear in the field equations. In this paper we extend this theory to any dimensions and discuss the thick braneworld model in five dimensions. Domain wall solutions are obtained numerically. The stability of the brane system under the tensor perturbation is analyzed. We find that the system is stable under the tensor perturbation and the gravity zero mode is localized on the brane. Therefore, the four-dimensional Newtonian potential can be realized on the brane.Comment: 7 pages, 4 figure

Image Restoration Using Very Deep Convolutional Encoder-Decoder Networks with Symmetric Skip Connections

In this paper, we propose a very deep fully convolutional encoding-decoding framework for image restoration such as denoising and super-resolution. The network is composed of multiple layers of convolution and de-convolution operators, learning end-to-end mappings from corrupted images to the original ones. The convolutional layers act as the feature extractor, which capture the abstraction of image contents while eliminating noises/corruptions. De-convolutional layers are then used to recover the image details. We propose to symmetrically link convolutional and de-convolutional layers with skip-layer connections, with which the training converges much faster and attains a higher-quality local optimum. First, The skip connections allow the signal to be back-propagated to bottom layers directly, and thus tackles the problem of gradient vanishing, making training deep networks easier and achieving restoration performance gains consequently. Second, these skip connections pass image details from convolutional layers to de-convolutional layers, which is beneficial in recovering the original image. Significantly, with the large capacity, we can handle different levels of noises using a single model. Experimental results show that our network achieves better performance than all previously reported state-of-the-art methods.Comment: Accepted to Proc. Advances in Neural Information Processing Systems (NIPS'16). Content of the final version may be slightly different. Extended version is available at http://arxiv.org/abs/1606.0892