Extra Proximal-Gradient Inspired Non-local Network. (arXiv:1911.07144v1 [cs.CV])

Variational method and deep learning method are two mainstream powerful approaches to solve inverse problems in computer vision. To take advantages of advanced optimization algorithms and powerful representation ability of deep neural networks, we propose a novel deep network for image reconstruction. The architecture of this network is inspired by our proposed accelerated extra proximal…

Subcarrier Assignment Schemes Based on Q-Learning in Wideband Cognitive Radio Networks. (arXiv:1911.07149v1 [eess.SP])

Subcarrier assignment is of crucial importance in wideband cognitive radio (CR) networks. In order to tackle the challenge that the traditional optimization-based methods are inappropriate in the dynamic spectrum access environment, an independent Q-learning-based scheme is proposed for the case that the secondary users (SUs) cannot exchange information while a collaborative Q-learning-based scheme is proposed…

Exponentially slow motion of interface layers for the one-dimensional Allen-Cahn equation with nonlinear phase-dependent diffusivity. (arXiv:1911.06926v1 [math.AP])

This paper considers a one-dimensional generalized Allen-Cahn equation of the form \[ u_t = \varepsilon^2 (D(u)u_x)_x – f(u), \] where $\varepsilon>0$ is constant, $D=D(u)$ is a positive, uniformly bounded below diffusivity coefficient that depends on the phase field $u$ and $f(u)$ is a reaction function that can be derived from a double-well potential with minima…

A class of quasilinear second order partial differential equations which describe spherical or pseudospherical surfaces. (arXiv:1911.06927v1 [math.DG])

Second order partial differential equations which describe spherical surfaces (ss) or pseudospherical surfaces (pss) are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature $K = 1$ or $K = -1$, respectively, and they can be seen as the compatibility condition of an associated su(2)-valued or sl(2, R)-valued linear…

Thin subgroups isomorphic to Gromov–Piateski-Shapiro lattices. (arXiv:1911.06933v1 [math.GT])

In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in $\mathrm{SO}(n,1)$ constructed by Gromov and Piateski-Shapiro can be embedded into $\mathrm{SL}_{n+1}(\mathbb{R})$ so that their images are thin subgroups

Classes of barren extensions. (arXiv:1911.06936v1 [math.LO])

Henle, Mathias, and Woodin proved that, provided that $\omega\rightarrow(\omega)^{\omega}$ holds in a model $M$ of ZF, then forcing with $([\omega]^{\omega},\subseteq^*)$ over $M$ adds no new sets of ordinals, thus earning the name a “barren” extension. Moreover, under an additional assumption, they proved that this generic extension preserves all strong partition cardinals. This forcing thus produces…

Infinite energy equivariant harmonic maps, domination, and anti-de Sitter $3$-manifolds. (arXiv:1911.06937v1 [math.DG])

We generalize a well-known existence and uniqueness result for equivariant harmonic maps due to Corlette, Donaldson, and Labourie to a non-compact infinite energy setting and analyze the asymptotic behaviour of the harmonic maps. When the relevant representation is Fuchsian and has hyperbolic monodromy, our construction recovers a family of harmonic maps originally studied by Wolf.…

The Overlap Gap Property and Approximate Message Passing Algorithms for $p$-spin models. (arXiv:1911.06943v1 [math.PR])

We consider the algorithmic problem of finding a near ground state (near optimal solution) of a $p$-spin model. We show that for a class of algorithms broadly defined as Approximate Message Passing (AMP), the presence of the Overlap Gap Property (OGP), appropriately defined, is a barrier. We conjecture that when $p\ge 4$ the model does…

Topological based classification using graph convolutional networks. (arXiv:1911.06892v1 [cs.SI])

In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological features of the nodes. We use this association to improve Graph machine learning in general and specifically, Graph Convolutional…

Imitation in the Imitation Game. (arXiv:1911.06893v1 [cs.CY])

We discuss the objectives of automation equipped with non-trivial decision making, or creating artificial intelligence, in the financial markets and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant. For this unintentional yet welcome aftereffect to set in a foundational list of…