Field Induced Jet Micro-EDM

Electrical discharge machining (EDM) is of the potential of micro/nano meter scale machining capability. However, electrode wear in micro-EDM significantly deteriorates the machining accuracy, thus, it needs to be compensated in process. To solve this problem, a novel micromachining method, namely field induced jet micro-EDM, is proposed in this paper, in which the electrical field induced jet is used as the micro tool electrode. A series of experiments were carried out to investigate the feasibility of proposed method. Due to the electrolyte can be supplied automatically by the capillary effect and the electrostatic field, it is not necessary to use pump or valves. The problem of electrode wear does not exist at all in the machining process because of the field induced jet will be generated periodically. It is also found that the workpiece material can be effectively removed with a crater size of about 2 micrometer in diameter. The preliminary experimental results verified that the field induced jet micro-EDM is an effective micromachining method

Top-N Recommender System via Matrix Completion

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relaxation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strategy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level.Comment: AAAI 201

Manipulation of electronic and magnetic properties of M2_2C (M=Hf, Nb, Sc, Ta, Ti, V, Zr) monolayer by applying mechanical strains

Tuning the electronic and magnetic properties of a material through strain engineering is an effective strategy to enhance the performance of electronic and spintronic devices. Recently synthesized two-dimensional transition metal carbides M$_2$C (M=Hf, Nb, Sc, Ta, Ti, V, Zr), known as MXenes, has aroused increasingly attentions in nanoelectronic technology due to their unusual properties. In this paper, first-principles calculations based on density functional theory are carried out to investigate the electronic and magnetic properties of M$_2$C subjected to biaxial symmetric mechanical strains. At the strain-free state, all these MXenes exhibit no spontaneous magnetism except for Ti$_2$C and Zr$_2$C which show a magnetic moment of 1.92 and 1.25 $\mu_B$/unit, respectively. As the tensile strain increases, the magnetic moments of MXenes are greatly enhanced and a transition from nonmagnetism to ferromagnetism is observed for those nonmagnetic MXenes at zero strains. The most distinct transition is found in Hf$_2$C, in which the magnetic moment is elevated to 1.5 $\mu_B$/unit at a strain of 15%. We further show that the magnetic properties of Hf$_2$C are attributed to the band shift mainly composed of Hf(5$d$) states. This strain-tunable magnetism can be utilized to design future spintronics based on MXenes

Graphs with 3-rainbow index n−1n-1 and n−2n-2

Let $G$ be a nontrivial connected graph with an edge-coloring $c:E(G)\rightarrow \{1,2,\ldots,q\},$ $q\in \mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color. For a vertex set $S\subseteq V(G)$, the tree connecting $S$ in $G$ is called an $S$-tree. The minimum number of colors that are needed in an edge-coloring of $G$ such that there is a rainbow $S$-tree for each $k$-set $S$ of $V(G)$ is called the $k$-rainbow index of $G$, denoted by $rx_k(G)$. In \cite{Zhang}, they got that the $k$-rainbow index of a tree is $n-1$ and the $k$-rainbow index of a unicyclic graph is $n-1$ or $n-2$. So there is an intriguing problem: Characterize graphs with the $k$-rainbow index $n-1$ and $n-2$. In this paper, we focus on $k=3$, and characterize the graphs whose 3-rainbow index is $n-1$ and $n-2$, respectively.Comment: 14 page

Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.Comment: Published in AAAI 201