On Multi-Relational Link Prediction with Bilinear Models

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can provide good prediction performance. The main goal of this paper is to explore the expressiveness of and the connections between various bilinear models proposed in the literature. In particular, a substantial number of models can be represented as bilinear models with certain additional constraints enforced on the embeddings. We explore whether or not these constraints lead to universal models, which can in principle represent every set of relations, and whether or not there are subsumption relationships between various models. We report results of an independent experimental study that evaluates recent bilinear models in a common experimental setup. Finally, we provide evidence that relation-level ensembles of multiple bilinear models can achieve state-of-the art prediction performance

Dynamic 3D shape measurement based on the phase-shifting moir\'e algorithm

In order to increase the efficiency of phase retrieval,Wang proposed a high-speed moire phase retrieval method.But it is used only to measure the tiny object. In view of the limitation of Wang method,we proposed a dynamic three-dimensional (3D) measurement based on the phase-shifting moire algorithm.First, four sinusoidal fringe patterns with a pi/2 phase-shift are projected on the reference plane and acquired four deformed fringe patterns of the reference plane in advance. Then only single-shot deformed fringe pattern of the tested object is captured in measurement process.Four moire fringe patterns can be obtained by numerical multiplication between the the AC component of the object pattern and the AC components of the reference patterns respectively. The four low-frequency components corresponding to the moire fringe patterns are calculated by the complex encoding FT (Fourier transform) ,spectrum filtering and inverse FT.Thus the wrapped phase of the object can be determined in the tangent form from the four phase-shifting moire fringe patterns using the four-step phase shifting algorithm.The continuous phase distribution can be obtained by the conventional unwrapping algorithm. Finally, experiments were conducted to prove the validity and feasibility of the proposed method. The results are analyzed and compared with those of Wang method, demonstrating that our method not only can expand the measurement scope, but also can improve accuracy.Comment: 14 pages,5 figures. ams.or

Linear subspaces of the intersection of two quadrics via Kuznetsov component

Let $Q_i(i=1,2)$ be $2g$ dimensional quadrics in $\mathbb{P}^{2g+1}$ and let $Y$ be the smooth intersection $Q_1\cap Q_2$. We associate the linear subspace in $Y$ with vector bundles on the hyperelliptic curve $C$ of genus $g$ by the left adjoint functor of $\Phi:D^b(C)\rightarrow D^b(Y)$. As an application, we give a different proof of the classification of line bundles and stable bundles of rank $2$ on hyperelliptic curves given by Desale and Ramanan. When $g=3$, we show that the projection functor induces a closed embedding $\alpha:Y\rightarrow SU^s_C(4,h)$ into the moduli space of stable bundles on $C$ of rank $4$ of fixed determinant.Comment: 15 page

Improved method for phase wraps reduction in profilometry

In order to completely eliminate, or greatly reduce the number of phase wraps in 2D wrapped phase map, Gdeisat et al. proposed an algorithm, which uses shifting the spectrum towards the origin. But the spectrum can be shifted only by an integer number, meaning that the phase wraps reduction is often not optimal. In addition, Gdeisat's method will take much time to make the Fourier transform, inverse Fourier transform, select and shift the spectral components. In view of the above problems, we proposed an improved method for phase wraps elimination or reduction. First, the wrapped phase map is padded with zeros, the carrier frequency of the projected fringe is determined by high resolution, which can be used as the moving distance of the spectrum. And then realize frequency shift in spatial domain. So it not only can enable the spectrum to be shifted by a rational number when the carrier frequency is not an integer number, but also reduce the execution time. Finally, the experimental results demonstrated that the proposed method is feasible.Comment: 16 pages, 15 figures, 1 table. arXiv admin note: text overlap with arXiv:1604.0723