Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces

This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. Appl. Math. 2002]. We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first order convergence rate.Comment: 52 page

Fractional stochastic differential equations satisfying fluctuation-dissipation theorem

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors

Language-Based Image Editing with Recurrent Attentive Models

We investigate the problem of Language-Based Image Editing (LBIE). Given a source image and a natural language description, we want to generate a target image by editing the source image based on the description. We propose a generic modeling framework for two sub-tasks of LBIE: language-based image segmentation and image colorization. The framework uses recurrent attentive models to fuse image and language features. Instead of using a fixed step size, we introduce for each region of the image a termination gate to dynamically determine after each inference step whether to continue extrapolating additional information from the textual description. The effectiveness of the framework is validated on three datasets. First, we introduce a synthetic dataset, called CoSaL, to evaluate the end-to-end performance of our LBIE system. Second, we show that the framework leads to state-of-the-art performance on image segmentation on the ReferIt dataset. Third, we present the first language-based colorization result on the Oxford-102 Flowers dataset.Comment: Accepted to CVPR 2018 as a Spotligh

State Space-Based Method for the DOA Estimation by the Forward-Backward Data Matrix Using Small Snapshots

In this presentation, a new low computational burden method for the direction of arrival (DOA) estimation from noisy signal using small snapshots is presented. The approach introduces State Space-based Method (SSM) to represent the received array signal, and uses small snapshots directly to form the Hankel data matrix. Those Hankel data matrices are then utilized to construct forward-backward data matrix that is used to estimate the state space model parameters from which the DOA of the incident signals can be extracted. In contrast to existing methods, such as MUSIC, Root-MUSIC that use the covariance data matrix to estimate the DOA and the sparse representation (SR) based DOA which is obtained by solving the sparsest representation of the snapshots, the SSM algorithm employs forward-backward data matrix formed only using small snapshots and doesn't need additional spatial smoothing method to process coherent signals. Three numerical experiments are employed to compare the performance among the SSM, Root-MUSIC and SR-based method as well as Cramér–Rao bound (CRB). The simulation results demonstrate that when a small number of snapshots, even a single one, are used, the SSM always performs better than the other two method no matter under the circumstance of uncorrelated or correlated signal. The simulation results also show that the computational burden is reduced significantly and the number of antenna elements is saved greatly