On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems

We obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known results (\cite{AR,PS1,PS2,Qi,Wil}). Moreover, by our new mountain pass theorem, new existence of nontrivial periodic solutions for some nonlinear second-order discrete systems is obtained, which greatly improves the result in \cite{Z04}.Comment: 11 page

End-to-End Photo-Sketch Generation via Fully Convolutional Representation Learning

Sketch-based face recognition is an interesting task in vision and multimedia research, yet it is quite challenging due to the great difference between face photos and sketches. In this paper, we propose a novel approach for photo-sketch generation, aiming to automatically transform face photos into detail-preserving personal sketches. Unlike the traditional models synthesizing sketches based on a dictionary of exemplars, we develop a fully convolutional network to learn the end-to-end photo-sketch mapping. Our approach takes whole face photos as inputs and directly generates the corresponding sketch images with efficient inference and learning, in which the architecture are stacked by only convolutional kernels of very small sizes. To well capture the person identity during the photo-sketch transformation, we define our optimization objective in the form of joint generative-discriminative minimization. In particular, a discriminative regularization term is incorporated into the photo-sketch generation, enhancing the discriminability of the generated person sketches against other individuals. Extensive experiments on several standard benchmarks suggest that our approach outperforms other state-of-the-art methods in both photo-sketch generation and face sketch verification.Comment: 8 pages, 6 figures. Proceeding in ACM International Conference on Multimedia Retrieval (ICMR), 201