Single Image Super-Resolution Using Multi-Scale Convolutional Neural Network

Methods based on convolutional neural network (CNN) have demonstrated tremendous improvements on single image super-resolution. However, the previous methods mainly restore images from one single area in the low resolution (LR) input, which limits the flexibility of models to infer various scales of details for high resolution (HR) output. Moreover, most of them train a specific model for each up-scale factor. In this paper, we propose a multi-scale super resolution (MSSR) network. Our network consists of multi-scale paths to make the HR inference, which can learn to synthesize features from different scales. This property helps reconstruct various kinds of regions in HR images. In addition, only one single model is needed for multiple up-scale factors, which is more efficient without loss of restoration quality. Experiments on four public datasets demonstrate that the proposed method achieved state-of-the-art performance with fast speed

Simple Systems with Anomalous Dissipation and Energy Cascade

We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems support dissipative solutions (suitably defined) and, as a result, may admit unique (statistical) steady states when the forcing term is nonzero. This claim is demonstrated via the complete characterization of the solutions of the system above for specific choices of the coupling coefficients. The mechanism of anomalous dissipations is shown to arise via a cascade of the energy towards the modes ($a_n$) with higher $n$; this is responsible for solutions with interesting energy spectra, namely \EE |a_n|^2 scales as $n^{-\alpha}$ as $n\to\infty$. Here the exponents $\alpha$ depend on the coupling coefficients $c_n$ and \EE denotes expectation with respect to the equilibrium measure. This is reminiscent of the conjectured properties of the solutions of the Navier-Stokes equations in the inviscid limit and their accepted relationship with fully developed turbulence. Hence, these simple models illustrate some of the heuristic ideas that have been advanced to characterize turbulence, similar in that respect to the random passive scalar or random Burgers equation, but even simpler and fully solvable.Comment: 32 Page

Modeling Chromosomes in Mouse to Explore the Function of Genes, Genomic Disorders, and Chromosomal Organization

One of the challenges of genomic research after the completion of the human genome project is to assign a function to all the genes and to understand their interactions and organizations. Among the various techniques, the emergence of chromosome engineering tools with the aim to manipulate large genomic regions in the mouse model offers a powerful way to accelerate the discovery of gene functions and provides more mouse models to study normal and pathological developmental processes associated with aneuploidy. The combination of gene targeting in ES cells, recombinase technology, and other techniques makes it possible to generate new chromosomes carrying specific and defined deletions, duplications, inversions, and translocations that are accelerating functional analysis. This review presents the current status of chromosome engineering techniques and discusses the different applications as well as the implication of these new techniques in future research to better understand the function of chromosomal organization and structures

Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl

Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.Comment: 32 page

Chronic Treatment with a Promnesiant GABA-A α5-Selective Inverse Agonist Increases Immediate Early Genes Expression during Memory Processing in Mice and Rectifies Their Expression Levels in a Down Syndrome Mouse Model

Decrease of GABAergic transmission has been proposed to improve memory functions. Indeed, inverse agonists selective for α5 GABA-A-benzodiazepine receptors (α5IA) have promnesiant activity. Interestingly, we have recently shown that α5IA can rescue cognitive deficits in Ts65Dn mice, a Down syndrome mouse model with altered GABAergic transmission. Here, we studied the impact of chronic treatment with α5IA on gene expression in the hippocampus of Ts65Dn and control euploid mice after being trained in the Morris water maze task. In euploid mice, chronic treatment with α5IA increased IEGs expression, particularly of c-Fos and Arc genes. In Ts65Dn mice, deficits of IEGs activation were completely rescued after treatment with α5IA. In addition, normalization of Sod1 overexpression in Ts65Dn mice after α5IA treatment was observed. IEG expression regulation after α5IA treatment following behavioral stimulation could be a contributing factor for both the general promnesiant activity of α5IA and its rescuing effect in Ts65Dn mice alongside signaling cascades that are critical for memory consolidation and cognition

Specific targeting of the GABA-A receptor α5 subtype by a selective inverse agonist restores cognitive deficits in Down syndrome mice

An imbalance between inhibitory and excitatory neurotransmission has been proposed to contribute to altered brain function in individuals with Down syndrome (DS). Gamma-aminobutyric acid (GABA) is the major inhibitory neurotransmitter in the central nervous system and accordingly treatment with GABA-A antagonists can efficiently restore cognitive functions of Ts65Dn mice, a genetic model for DS. However, GABA-A antagonists are also convulsant which preclude their use for therapeutic intervention in DS individuals. Here, we have evaluated safer strategies to release GABAergic inhibition using a GABA-A-benzodiazepine receptor inverse agonist selective for the α5-subtype (α5IA). We demonstrate that α5IA restores learning and memory functions of Ts65Dn mice in the novel-object recognition and in the Morris water maze tasks. Furthermore, we show that following behavioural stimulation, α5IA enhances learning-evoked immediate early gene products in specific brain regions involved in cognition. Importantly, acute and chronic treatments with α5IA do not induce any convulsant or anxiogenic effects that are associated with GABA-A antagonists or non-selective inverse agonists of the GABA-A-benzodiazepine receptors. Finally, chronic treatment with α5IA did not induce histological alterations in the brain, liver and kidney of mice. Our results suggest that non-convulsant α5-selective GABA-A inverse agonists could improve learning and memory deficits in DS individuals

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe

Macroscopic models for superconductivity

This paper reviews the derivation of some macroscopic models for superconductivity and also some of the mathematical challenges posed by these models. The paper begins by exploring certain analogies between phase changes in superconductors and those in solidification and melting. However, it is soon found that there are severe limitations on the range of validity of these analogies and outside this range many interesting open questions can be posed about the solutions to the macroscopic models

Global generalized solutions for Maxwell-alpha and Euler-alpha equations

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit