Two questions on stable equivalences of Morita type

It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.Comment: 9 page

The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form

Let $M=S^n/ \Gamma$ and $h$ be a nontrivial element of finite order $p$ in $\pi_1(M)$, where the integer $n\geq2$, $\Gamma$ is a finite group which acts freely and isometrically on the $n$-sphere and therefore $M$ is diffeomorphic to a compact space form. In this paper, we establish first the resonance identity for non-contractible homologically visible minimal closed geodesics of the class $[h]$ on every Finsler compact space form $(M, F)$ when there exist only finitely many distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$ with a bumpy Finsler metric, which improves a result of Taimanov in [Taimanov 2016] by removing some additional conditions. Also our results extend the resonance identity and multiplicity results on $\mathcal{R}P^n$ in [arXiv:1607.02746] to general compact space forms.Comment: 33 pages, All comments are welcome. arXiv admin note: substantial text overlap with arXiv:1607.0274

Deep Sketch Hashing: Fast Free-hand Sketch-Based Image Retrieval

Free-hand sketch-based image retrieval (SBIR) is a specific cross-view retrieval task, in which queries are abstract and ambiguous sketches while the retrieval database is formed with natural images. Work in this area mainly focuses on extracting representative and shared features for sketches and natural images. However, these can neither cope well with the geometric distortion between sketches and images nor be feasible for large-scale SBIR due to the heavy continuous-valued distance computation. In this paper, we speed up SBIR by introducing a novel binary coding method, named \textbf{Deep Sketch Hashing} (DSH), where a semi-heterogeneous deep architecture is proposed and incorporated into an end-to-end binary coding framework. Specifically, three convolutional neural networks are utilized to encode free-hand sketches, natural images and, especially, the auxiliary sketch-tokens which are adopted as bridges to mitigate the sketch-image geometric distortion. The learned DSH codes can effectively capture the cross-view similarities as well as the intrinsic semantic correlations between different categories. To the best of our knowledge, DSH is the first hashing work specifically designed for category-level SBIR with an end-to-end deep architecture. The proposed DSH is comprehensively evaluated on two large-scale datasets of TU-Berlin Extension and Sketchy, and the experiments consistently show DSH's superior SBIR accuracies over several state-of-the-art methods, while achieving significantly reduced retrieval time and memory footprint.Comment: This paper will appear as a spotlight paper in CVPR201

Two-dimensional finite-difference model for moving boundary hydrodynamic problems

To predict the hydrodynamics of lakes, estuaries and shallow seas, a two 'dimensional numerical model is developed using the method of fractional steps. The governing equations, i.e., the vertically integrated Navier-Stokes equations of fluid motion, are solved through three steps: advection, diffusion and propagation. The characteristics method is used to solve the advection, the alternating direction implicit method is applied to compute the diffusion, and the conjugate gradient iterative method is employed to calculate the propagation. Two ways to simulate the moving boundary problem are studied. The first method is based on the weir formulation. The second method is based on the assumption that a thin water layer exists over the entire dry region at all times. A number of analytical solutions are used to validate the model. The model is also applied to simulate the wind driven circulation in Lake Okeechobee, Florida. (135 page document