Learning a Mixture of Deep Networks for Single Image Super-Resolution

Single image super-resolution (SR) is an ill-posed problem which aims to recover high-resolution (HR) images from their low-resolution (LR) observations. The crux of this problem lies in learning the complex mapping between low-resolution patches and the corresponding high-resolution patches. Prior arts have used either a mixture of simple regression models or a single non-linear neural network for this propose. This paper proposes the method of learning a mixture of SR inference modules in a unified framework to tackle this problem. Specifically, a number of SR inference modules specialized in different image local patterns are first independently applied on the LR image to obtain various HR estimates, and the resultant HR estimates are adaptively aggregated to form the final HR image. By selecting neural networks as the SR inference module, the whole procedure can be incorporated into a unified network and be optimized jointly. Extensive experiments are conducted to investigate the relation between restoration performance and different network architectures. Compared with other current image SR approaches, our proposed method achieves state-of-the-arts restoration results on a wide range of images consistently while allowing more flexible design choices. The source codes are available in http://www.ifp.illinois.edu/~dingliu2/accv2016

Recursive relations for a quiver gauge theory

We study the recursive relations for a quiver gauge theory with the gauge group $SU(N_1)\times SU(N_2)$ with bifundamental fermions transforming as $(N_1,\bar{N_2})$. We work out the recursive relation for the amplitudes involving a pair of quark and antiquark and gluons of each gauge group. We realize directly in the recursive relations the invariance under the order preserving permutations of the gluons of the first and the second gauge group. We check the proposed relations for MHV, 6-point and 7-point amplitudes and find the agreements with the known results and the known relations with the single gauge group amplitudes. The proposed recursive relation is much more efficient in calculating the amplitudes than using the known relations with the amplitudes of the single gauge group.Comment: 33 pages and 2 figures, minor correction

Highly Stretchable MoS2_2 Kirigami

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS$_{2}$ kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key finding is significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS$_{2}$ nanoribbons. These results in conjunction with recent results on graphene suggest that the kirigami approach may be a generally useful one for enhancing the ductility of two-dimensional nanomaterials

Polarization and valley switching in monolayer group-IV monochalcogenides

Group-IV monochalcogenides are a family of two-dimensional puckered materials with an orthorhombic structure that is comprised of polar layers. In this article, we use first principles calculations to show the multistability of monolayer SnS and GeSe, two prototype materials where the direction of the puckering can be switched by application of tensile stress or electric field. Furthermore, the two inequivalent valleys in momentum space, which are dictated by the puckering orientation, can be excited selectively using linearly polarized light, and this provides an additional tool to identify the polarization direction. Our findings suggest that SnS and GeSe monolayers may have observable ferroelectricity and multistability, with potential applications in information storage

Exotic Smooth Structures on Small 4-Manifolds

Let M be either CP^2#3CP^2bar or 3CP^2#5CP^2bar. We construct the first example of a simply-connected symplectic 4-manifold that is homeomorphic but not diffeomorphic to M.Comment: 11 page

Accelerated search and design of stretchable graphene kirigami using machine learning

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks, commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of ∼4×106 candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.P. Z. H. developed the codes, performed the simulations and data analysis, and wrote the manuscript with input from all authors. P. Z. H. and E. D. C. developed the machine learning methods. P. Z. H., D. K. C. and H. S. P. acknowledge the Hariri Institute Research Incubation Grant No. 2018-02-002 and the Boston University High Performance Shared Computing Cluster. P. Z. H. is grateful for the Hariri Graduate Fellowship. P. Z. H. thank Grace Gu and Adrian Yi for helpful discussions. (2018-02-002 - Hariri Graduate Fellowship)Published versio