Some properties on GG-evaluation and its applications to GG-martingale decomposition

In this article, a sublinear expectation induced by $G$-expectation is introduced, which is called $G$-evaluation for convenience. As an application, we prove that any $\xi\in L^\beta_G(\Omega_T)$ with some $\beta>1$ the decomposition theorem holds and any $\beta>1$ integrable symmetric $G$-martingale can be represented as an It$\hat{o}'s$ integral w.r.t $G$-Brownian motion. As a byproduct, we prove a regular property for $G$-martingale: Any $G$-martingale $\{M_t\}$ has a quasi-continuous versionComment: 22 page

Covariant entropy conjecture and concordance cosmological models

Recently a covariant entropy conjecture has been proposed for dynamical horizons. We apply this conjecture to concordance cosmological models, namely, those cosmological models filled with perfect fluids, in the presence of a positive cosmological constant. As a result, we find this conjecture has a severe constraint power. Not only does this conjecture rule out those cosmological models disfavored by the anthropic principle, but also it imposes an upper bound $10^{-60}$ on the cosmological constant for our own universe, which thus provides an alternative macroscopic perspective for understanding the long-standing cosmological constant problem.Comment: 10 pages, 1 figure, JHEP style, references added, published versio

Deep Expander Networks: Efficient Deep Networks from Graph Theory

Efficient CNN designs like ResNets and DenseNet were proposed to improve accuracy vs efficiency trade-offs. They essentially increased the connectivity, allowing efficient information flow across layers. Inspired by these techniques, we propose to model connections between filters of a CNN using graphs which are simultaneously sparse and well connected. Sparsity results in efficiency while well connectedness can preserve the expressive power of the CNNs. We use a well-studied class of graphs from theoretical computer science that satisfies these properties known as Expander graphs. Expander graphs are used to model connections between filters in CNNs to design networks called X-Nets. We present two guarantees on the connectivity of X-Nets: Each node influences every node in a layer in logarithmic steps, and the number of paths between two sets of nodes is proportional to the product of their sizes. We also propose efficient training and inference algorithms, making it possible to train deeper and wider X-Nets effectively. Expander based models give a 4% improvement in accuracy on MobileNet over grouped convolutions, a popular technique, which has the same sparsity but worse connectivity. X-Nets give better performance trade-offs than the original ResNet and DenseNet-BC architectures. We achieve model sizes comparable to state-of-the-art pruning techniques using our simple architecture design, without any pruning. We hope that this work motivates other approaches to utilize results from graph theory to develop efficient network architectures.Comment: ECCV'1

Quantum Entanglement of Electromagnetic Fields in Non-inertial Reference Frames

Recently relativistic quantum information has received considerable attention due to its theoretical importance and practical application. Especially, quantum entanglement in non-inertial reference frames has been studied for scalar and Dirac fields. As a further step along this line, we here shall investigate quantum entanglement of electromagnetic fields in non-inertial reference frames. In particular, the entanglement of photon helicity entangled state is extensively analyzed. Interestingly, the resultant logarithmic negativity and mutual information remain the same as those for inertial reference frames, which is completely different from that previously obtained for the particle number entangled state.Comment: more explanatory material added in the introduction, version to appear in Journal of Physics

Bioinspired Multifunctional Anti-icing Hydrogel

The recent anti-icing strategies in the state of the art mainly focused on three aspects: inhibiting ice nucleation, preventing ice propagation, and decreasing ice adhesion strength. However, it is has proved difficult to prevent ice nucleation and propagation while decreasing adhesion simultaneously, due to their highly distinct, even contradictory design principles. In nature, anti-freeze proteins (AFPs) offer a prime example of multifunctional integrated anti-icing materials that excel in all three key aspects of the anti-icing process simultaneously by tuning the structures and dynamics of interfacial water. Here, inspired by biological AFPs, we successfully created a multifunctional anti-icing material based on polydimethylsiloxane-grafted polyelectrolyte hydrogel that can tackle all three aspects of the anti-icing process simultaneously. The simplicity, mechanical durability, and versatility of these smooth hydrogel surfaces make it a promising option for a wide range of anti-icing applications

Revisiting f(R) gravity models that reproduce Λ\LambdaCDM expansion

We reconstruct an $f(R)$ gravity model that gives rise to the particular $\Lambda$CDM background evolution of the universe. We find well-defined, real-valued analytical forms for the $f(R)$ model to describe the universe both in the early epoch from the radiation to matter dominated eras and the late time acceleration period. We further examine the viability of the derived $f(R)$ model and find that it is viable to describe the evolution of the universe in the past and there does not exist the future singularity in the Lagrangian.Comment: 7 pages, 2 figures, revised version, accepted for publication in PR

Superpixel Convolutional Networks using Bilateral Inceptions

In this paper we propose a CNN architecture for semantic image segmentation. We introduce a new 'bilateral inception' module that can be inserted in existing CNN architectures and performs bilateral filtering, at multiple feature-scales, between superpixels in an image. The feature spaces for bilateral filtering and other parameters of the module are learned end-to-end using standard backpropagation techniques. The bilateral inception module addresses two issues that arise with general CNN segmentation architectures. First, this module propagates information between (super) pixels while respecting image edges, thus using the structured information of the problem for improved results. Second, the layer recovers a full resolution segmentation result from the lower resolution solution of a CNN. In the experiments, we modify several existing CNN architectures by inserting our inception module between the last CNN (1x1 convolution) layers. Empirical results on three different datasets show reliable improvements not only in comparison to the baseline networks, but also in comparison to several dense-pixel prediction techniques such as CRFs, while being competitive in time.Comment: European Conference on Computer Vision (ECCV), 201

Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

Some time ago Takahashi derived so called {\it transverse} relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He & Yu have given an indicative proof at one-loop level in 4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor defined only unambiguously in 4-dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one loop order in $d$-dimensions, with $d=4+\epsilon$.Comment: 20 pages, 3 figures This version corrects and clarifies the previous result. This version has been submitted for publicatio